Probability- Aptitude Questions and Answers

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Three unbiased coins are tossed, what is the probability of getting at least 2 tails ?

A)
1/3

B)
1/4

C)
1/2

D)
3/2


Correct Answer :

1/2


Explanation :

Sample space ,n(S) = {TTT, HHH, TTH, THT, HTT, THH, HTH, HHT} = 8
Let Event of getting at least 2 tails,n(E) = {TTH, THT, HTT, TTT} = 4

Probability P(E) = n(E)/n(S) = 4 / 8 = 1 / 2

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Find the probability that a leap year selected at random will contain 53 Sundays.

A)
5/7

B)
3/4

C)
4/7

D)
2/7


Correct Answer :

2/7


Explanation :

Total number of days in a leap year = 366
It will contain 52 full weeks 2 extra days ( 52* 7 days in week + 2 days= 366 days)
Sample space for 2 extra days is n(S): {sun-mon, mon-tue, tue-wed, wed-thu, thu-fri, fri-sat, sat-sun} = 7
Out of these only two outcomes n(A): { sat-sun} and {sun-mon} is having sunday with them = 2

Therefore, probability that a leap year has 53 Sundays = n(A)/n(S) = 2/7

There are 5 red and 7 blue balls in a bucket. If one ball is drawn at random from the bucket then what is the probability that the ball drawn will be of red colour?

A)
5/12

B)
7/12

C)
1/2

D)
1/12


Correct Answer :

5/12


Explanation :

total numbers of balls in bucket = 5 red+7 blue=12
sample space n(S)=number of ways of drawing one ball out of 12=12C1=>12
event of drawn one red ball out of 5 red balls n(E)=5C1=>5

hence probability p(E)=n(E)/n(S)=5/12

Two dices are thrown randomly. Find the probability of getting the sum of digits as 9.

A)
1/6

B)
1/9

C)
1/12

D)
None of these


Correct Answer :

1/9


Explanation :

All possible outcome when two dices are thrown randomly =sample space is n(S)=(6*6)=36 outcomes
event of getting the sum of digits as 9 are n(E) ={(3,6),(4,5),(5,4),(6,3)}=4 outcomes

Therefore Probability P(E)=n(E)/n(S)=4/36=1/9

A bag contains 2 red marbles, 3 green marbles and 4 blue marbles. A marble is picked at random from the bag. What is the probability that the marble is not a blue marble?

A)
4/9

B)
5/9

C)
1/9

D)
2/3


Correct Answer :

5/9


Explanation :

total numbers of marbles in bag = 2 red+3 green+4 blue=9
sample space n(S)=number of ways of drawing one marble out of 9 marble from bag=9C1=>9
event of picking one marble which is not a blue
that is picking one marble from out of (2 red+3 green) 5 marbles, n(E)=5C1=>5

hence probability p(E)=n(E)/n(S)=5/9

A coin is tossed. What is the probability of getting a head or a tail?

A)
0

B)
1

C)
1/2

D)
1/4


Correct Answer :

1


Explanation :

When coin is tossed, result will be either heads or tails.there

Total number of possible outcomes i.e. sample space n(S) : {H,T} = 2
event of getting outcomes either heads or tails n(E): {H,T} = 2

So number of probable outcomes and total number of outcomes are same i.e. 2.

So, probability of getting either heads or tails when a coin is tossed once
=> Number of favourable outcomes/Total number of possible outcomes
=> n(E)/n(S) = 2/2 = 1

Note:
Probability of getting heads when a coin is tossed once = 1/2
Probability of getting tails when a coin is tossed once = 1/2

In a box there are 4 black, 4 orange and 2 blue marbles. Two marbles are drawn at random. What is the probability that at least one marble is of blue colour?

A)
4/5

B)
3/5

C)
1/5

D)
None of these


Correct Answer :

None of these


Explanation :

total numbers of marbles in box= 4 black+4 orange+2 blue=10 marbles
sample space n(S)=number of ways of drawing two marbles out of 10 marbles from box= 10C2 =10!/2!*8! =10*9/2*1 =45
event of picking two marble those are not blue from out of (4 black+4 orange) 8 marbles, n(E)=8C2=8!/2!*6! =8*7/2*1=28

hence probability of drawn two marble from box which not blue p(E)=n(E)/n(S)=28/45
So probability to drown atleast one marble is blue=1-28/45=(45-28)/45=37/45

A box contains 9 red, 7 white and 4 black balls. A ball is drawn at random. What is the probability that the ball drawn is not red ?

A)
1/11

B)
9/20

C)
2/11

D)
11/20


Correct Answer :

11/20


Explanation :

total numbers of balls in bucket =9 red + 7 white + 4 black=20
sample space n(S)=number of ways of drawing one ball out of 20=20C1=>20
event of drawn one red ball out of 9 red balls n(E)=9C1=>9

Hence probability p(E)=n(E)/n(S)=9/20
And probability that the ball drawn is not red , P(not-red) = (1 - 9/20) = 11/20

A number is chosen at random among the first 120 natural numbers. The probability of the number chosen being a multiple of 5 or 15 is ?

A)
1/5

B)
1/8

C)
1/6

D)
1/12


Correct Answer :

1/5


Explanation :

sample space n(S)=number of ways chosen at random among the first 120 natural numbers=>120
event space n(E) =number chosen being a multiple of 5 or 15 i,e., (5, 10, ...,25, 30, ..50..,100, 105, 110, 115, 120)
Tn=2a+(n-1)d , a=5 d=5
120=4+(n−1)5
n=24
Hence probability p(E)=n(E)/n(S)=24/120 =1/5

A single letter is selected at random from the word 'PROBABILITY'. The probability that it is a vowel, is?

A)
3/11

B)
4/11

C)
2/11

D)
1/11


Correct Answer :

4/11


Explanation :

Sample space n(S)=Total number of letters=>11
Event space n(E) =number of vowels in 'PROBABILITY' ie. (O,B,I,I) =4

Hence probability p(E)=n(E)/n(S)=4/11

If a number is chosen from the set {1, 2, 3…90}, then the probability that the chosen number is multiple of 7 is?

A)
1/6

B)
2/15

C)
1/12

D)
7/30


Correct Answer :

2/15


Explanation :

All possible outcome If a number is chosen from the set {1, 2, 3…90} =sample space is n(S)=90 ways
event of getting number is multiple of 7 is n(E) ={7,14,21.....70,77,84}=12 outcomes

Therefore Probability P(E)=n(E)/n(S)=12/90=2/15

A number is randomly selected from set A ={1,2,3,} and then second number is randomly selected from set B={1,3,9} The probability that the sum of the two numbers selected will be less than or equal to 4, is?

A)
1/3

B)
5/9

C)
2/3

D)
7/9


Correct Answer :

1/3


Explanation :

All possible outcome to select the number from both set and when do sum =sample space is n(S)={1+1,1+3,1+9,2+1,2+3,2+9,3+1,3+3,3+9}=9 ways
event of getting sum of the two numbers selected will be less than or equal to 4,n(E) ={1+1,1+3,2+1}=3 outcomes

Therefore Probability P(E)=n(E)/n(S)=3/9=1/3

Which of the following has the maximum probability to be the sum of the number on top face of two dice, when both the dice thrown together?

A)
7

B)
8

C)
9

D)
10


Correct Answer :

7


Explanation :

Outcomes for Two Dice

1 2 3 4 5 6
1 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
4 (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
6 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

the maximum probability to be the sum of the number on top face of two dice = maximum Outcomes for that number

7 =(6, 1) , (5, 2), (4, 3), (3, 4), (2, 5), (1, 6)
8 =(6, 2) , (5, 3), (4, 4), (3, 5), (2, 6)
9 =(6, 3) , (5, 4), (4, 5), (3, 6)
10 =(6, 4) , (5, 5), (4, 6)

Hence ,maximum probability that the sum of the two dice is seven

Two unbiased coins are tossed. What is probability of getting at most one tail ?

A)
5/4

B)
3/4

C)
1

D)
1/2


Correct Answer :

3/4


Explanation :

Sample space , n(S) = {HH, TT, TH, HT} = 4
Let Event of getting at most one tail,n(E) = {TT, TH, HT} = 3

Probability P(E) = n(E)/n(S) = 3 / 4

In a throw of dice what is the probability of getting number greater than 5 ?

A)
2/6

B)
1/2

C)
5/6

D)
1/6


Correct Answer :

1/6


Explanation :

Sample space ,n(S) = {1, 2, 3, 4, 5, 6} = 6
Let Event of getting number greater than 5,n(E) = {6} = 1

Probability P(E) = n(E)/n(S) = 1/ 6

There are 3 children in the Khanna's family and it is known that there is at least 1 girl among the 3 children. What is the probability that all 3 of them are girls?

A)
1/7

B)
1/8

C)
1/6

D)
2/7


Correct Answer :

1/7


Explanation :

Let G=girl, B=boy.
with three children, where each could either be a girl,the total number of possible combinations {GGG,GGB,GBG,BGG,GBB,BGB,BBG,BBB} = 8
If at least one is a girl we can rule out BBB (all boy)

thus sample space is, n(S) : {GGG,GGB,GBG,BGG,GBB,BGB,BBG} = 7
out of these only one outcomes is all girl, n(E): (GGG) = 1

Therefore, probability that all will be girl = n(E)/n(S) = 1/7

A card is drawn from a well shuffled pack of cards. What is the probability that it is a red card or a face card?

A)
19/26

B)
9/13

C)
8/13

D)
37/52


Correct Answer :

8/13


Explanation :

There are a total of 52 cards.
Now, there are 26 red cards and 12 face cards, 6 of which are red (double counted)

So, the probability of having a card's red card or face card
P(Red u King)=P(Red)+P(face)-P(Red n face)
=26/52 + 12/52 - 6/52
=32/52
=8/13

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Pipes and Cistern

Three taps A,B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternatively, the tank will be full in?

Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A s opened first, in how many hours, the tank shall be full?

A large tanker can be filled by two pipes A and B in 60 min and 40 min respectively. How many minutes will it take to fill the tanker from empty state if B is used for first half of the time, and A and B fill it together for the other half?

A tank is filled by 3 pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The 2nd pipe fills the tank 5 hours faster than first pipe and 4 hours slower than third pipe. The time required by first pipe is?

Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?

Two pipes A and B can fill a tank in 24 min and 32 min respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min?

Two pipes A and B can fill a tank in 36 min and 45 min respectively. A water pipe C can empty the tank in 30 min. First A and B are opened. after 7 min, C is also opened. In how much time, the tank is full?

Two pipes can fill a cistern in 14 hours and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom it took 32 min more to fill the cistern. When the cistern is full, in what time will the leak empty it?

Bucket P has thrice the capacity as Bucket Q. It takes 60 turns for Bucket P to fill the empty drum. How many turns it will take for both the buckets P and Q, having each turn together to fill the empty drum?

Probability

In a class , 30 % of the students offered English, 20 % offered Hindi and 10 % offered Both.If a student is offered at random, what is the probability that he has offered English or Hindi?

In a lottery ,there are 10 prizes and 25 blanks.A lottery is drawn at random. what is the probability of getting a prize ?

Two dice are thrown simultaneously .what is the probability of getting two numbers whose product is even?

Two diced are tossed the probability that the total score is a prime number?

Two cards are drawn at random from a pack of 52 cards What is the probability that either both are black or both are queens?

Two dice are thrown together .What is the probability that the sum of the number on the two faces is divisible by 4 or 6?

A bag contains 6 white and 4 black balls .Two balls are drawn at random .Find the probability that they are of the same colour?

In a simultaneous throw of a pair of dice,find the probability of getting a total more than 7?

An unbiased die is tossed.Find the probability of getting a multiple of 3?

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