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# Arithmetic Aptitude :: Probability

Home > Arithmetic Aptitude > Probability > General Questions

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1. In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

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Explanation:

Let's assume the sample space = S
and Event of selecting 1 girl and 2 boys = E

So, n(S) = Number ways of selecting 3 students out of 25 = 25C3
=> (25 * 24 * 23)/(3 * 2 * 1) = 2300.
n(E) = (10C1 * 15C2)
= 10 * [(15 * 14)/(2 * 1)] = 1050.
P(E) = n(E)/n(S) = 1050/2300 = 21/46.

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Tags:  IBM Global Edge

2. A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

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Explanation:

Solution: 2 red, 3 green, and 2 blue balls are there. So the probability of getting no blue ball is not selecting any blue ball among the two chosen balls hence 5C2.

5C2/7C2 = 10/21.

7C2 because we can select any 2 balls from 7 balls in that number of ways.

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3. 10 men and 10 women are there, they dance with each other, is there possibility that 2 men are dancing with same women and vice versa.

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Explanation:

how can anybody explain???

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Tags:  TCS Global Edge

4. There is a toy train that can make 10 musical sounds. It makes 2 musical sounds after being defective. What is the probability that same musical sound would be produced 5 times consecutively?

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Explanation:

1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32

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Tags:  TCS

5. There are 11 boys in a family. Youngest child is a boy. Probability is 1 that of all are boys out of?

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Explanation:

Solution: 11 boys, given youngest one is the boy

Probability of a boy or girl is (1/2)

Probability of finding remaining 10 children to get a boy is-

so (1/2)^10=1/1024.

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Tags:  TCS

6. For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A's chances of winning. Let's assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?

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Explanation:

Solution: Answer is 5/9 because for example

Let Paul picks Ghana then probability that its prophecy will be true is 2/3*2/3 =4/9.

Now it may pick up Bolivia and the chances of winning are 1/3*1/3=1/9

So total probability will be 4/9 1/9=5/9

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Tags:  TCS

7. After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?

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Explanation:

Solution:

If one letter is put in a wrong envelope, then one other letter must also be put in the wrong envelope. So zero is the probability that exactly 1 letter is inserted in an improper envelope because it's not possible.

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Tags:  TCS

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

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Explanation:

P (getting a prize) = 10/(10 + 25)
=> 10/35 = 2/7

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Tags:  nagarro

9. A 5-digit number is formed by the digits 2,4,5,6,8 (each digit used exactly once) . What is the probability that the number formed is divisible by 4 ?

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Explanation:

A no. is divisible by 4 if last two digit is divisible by 4
so numbers ending with 24,28,48,52,56,64,68,84 are divisible by 4
last two places are fixed by 24,28,48,52,56,64,68,84
so remaining 3 places can be filled in 3! ways for each
total=8*3!=48=n(E)
n(S) = 5!
so
= n(E)/n(S)
=48/120=2/5

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Tags:  Capgemini

10. A group consists of equal number of men and women. Of them 10% of men and 45% of women are unemployed. If a person is randomly selected from the group. Find the probability for the selected person to be an employee.

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