Conditional probability

Q.

The chances to fail in Physics are $20\%$ and the chances to fail in Mathematics are $10\%$. What are the chances to fail in at least one subject?

1. $28\%$

2. $38\%$

3. $72\%$

4. $82\%$

Q.

Assuming that for a husband wife couple the chances of their child being a boy or a girl are the same, the probability of their two children being a boy and a girl is

1. $\frac{1}{4}$

2. $1$

3. $\frac{1}{2}$

4. $\frac{1}{8}$

Q.

In four schools $\text{B1, B2, B3, B4}$ the percentage of girls students is $12,20,13,17$ respectively.

From a school selected at random, one student is picked up at random and it is found that the student is a girl.

The probability that the school selected is $\text{B2}$ is

1. $\frac{6}{31}$

2. $\frac{10}{31}$

3. $\frac{13}{62}$

4. $\frac{17}{62}$

Q. Two dice are thrown. The probability that the sum of the numbers coming up on them is 9, if it is known that the number 5 always occurs on the first die, is:

1. $\frac{1}{6}$
2. $\frac{1}{3}$
3. $\frac{2}{3}$
4. $None$

Q.

$6$ boys and $6$ girls are sitting in a row randomly. The probability that boys and girls sit alternately is:

1. $\frac{1}{36}$

2. $\frac{1}{462}$

3. $\frac{5}{126}$

4. $\frac{1}{231}$

Q. A box contains three coins: two regular coins and one fake two-headed coin (P(H)=1)
You pick a coin at random and toss it, and get heads. The probability that it is the two-headed coin = ___

Q. In a bag, there are 2 blue balls, 5 green balls and 6 red balls. If a person took two balls without replacement, what is the probability that the second ball will be red given that the first ball is red?

1. $\frac{5}{12}$
2. $\frac{1}{2}$
3. $\frac{6}{13}$
4. $\frac{30}{156}$

Q. One ticket is selected at random from 50 tickets numbered 00, 01, 02, ...., 49. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals

1. $\frac{5}{14}$
2. $\frac{1}{50}$
3. $\frac{1}{14}$
4. $\frac{1}{7}$

Q. Two dice are thrown. The probability that the sum of numbers coming up on them is 9, if it is known that the number 5 always occurs on the first die, is

1. $\frac{1}{6}$
2. $\frac{1}{3}$
3. $\frac{2}{3}$
4. $\frac{1}{4}$

Q. A and B are events such that $P\left(A\right)=0.3,P(A\cup B)=0.8$. If A and B are independent then P(B)=

1. $\frac{3}{7}$
2. $\frac{5}{7}$
3. $\frac{6}{7}$
4. $\frac{1}{7}$