# Question 2:

A and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins.                                              [CBSE Delhi 2016]

## Solution:

‘A’ getting sum 7 in pair of dice = (2, 5),(5, 2), (1, 6), (6, 1), (4, 3), (3, 4)

P(A getting the sum 7) = P(win) = 6/36 = 1/6

P(A not getting sum 7) = P( A lose) = 1 – 1/6 = 5/6

‘B’ getting sum 10 in pair of dice = (5, 5),(4, 6), (6, 4)

P(B getting the sum 10)   = P(B win)= 3/36 = 1/12

P(B not getting the sum 10) = P(B lose)= 1 – 1/12 = 11/12

P(B wins) = P(A lose).P(B wins) + P(A lose).P(B lose).P(A lose).P(B wins) + . . .

⇒ P(B wins)      # Question: 1

The probabilities of two students A and B coming to the school in time are 3/7 and 5/7 respectively. Assuming that the events, ‘A coming in time’ and ‘B coming in time’ are independent, find the probability of only one of them coming to the school in time.                                                                                                              [CBSE(AI)  2013]

# Question 3:

A, B and C throw a pair of dice in that order alternately till one of them gets a total of 9 and wins the game . Find their respective probabilities of winning, if A starts first.                                            [CBSE(East) 2016]

# Question 4:

The probability that A hits a target is 1/3 and the probability that B hits it is 2/5. If each one of A and B shoots at the target, what is the probability that                                                  [CBSE (F) 2009]

(i) The target is hit ?        (ii) Exactly one of them hits the target ?

# Question 5:

In a group of 50 scouts in a camp, 30 are well trained in first aid techniques while the remaining are well trained in hospitality but not in first aid. Two scouts are selected at random from the group. Find the probability distribution of number of selected scouts who are well trained in first aid . Find the mean of the distribution also.

Write one more value which is expected from a well trained scouts.

# Question 6:

A bag I contains 5 red and 4 white balls and a bag II contains 3 red and 3 white balls. Two balls are transferred from the bag I to the bag II and then one ball is drawn from the bag II. If the ball drawn from the bag II is red, then find the probability that one red and one white ball are transferred from the bag I to the bag II.               [CBSE Sample paper 2016] 