Bayes' Theorem

Q.

Two toys are drawn from a bag containing 21 toys numbered from 1 to 21 (without replacement). Find the probability that both the toys will show even numbers.

1. 

2. 

3. 

4. None of these

Q.

From a box containing 100 balls numbered from 1 to 100, three balls are selected at random with replacement from the box.
What is the probability that the sum of the three numbers on the balls selected from the box will be odd?

1. none

2. 1/3

3. 1/2

4. 3/4

5. 3/8

Q.

There are three similar boxes, containing:
(i) 5 black and 5 white balls
(ii) 3 black and 7 white balls
(iii) 6 black and 4 white balls, respectively.

Sarosh chooses one of the three boxes at random and from that particular box, he picks up a ball at random and finds that the ball is black.
What is the probability that the ball is picked up from the second box?

1. 9/14

2. 5/14

3. 11/14

4. 3/14

5. none

Q.

In a box, there are 9 red, 7 blue and 5 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

1. none

2. 11/21

3. 1/2

4. 10/21

5. 1/3

Q.

What is the probability of getting a spade and a clubwhen two cards are drawn together from a pack of 52 cards.

1. 13/102

2. 47/100

3. none

4. 13/51

5. 13/91

Q. The odds against A solving a certain problem are $4$ to $3$ and the odds in favour of B solving the same problem are $7$ to $5$. If both of them try independently, the probability that the problem will be solved is :

1. $\frac{11}{21}$
2. $\frac{13}{21}$
3. $\frac{16}{21}$
4. $\frac{8}{21}$