Probability- Aptitude Questions and Answers

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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

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

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

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