**Probability ncert solutions Chapter 15 Exercise 15.1 Question 15**

**15.** Five cards- the ten, jack, queen, king and ace of diamonds are well shuffled with their face downwards. One card is then picked up at random.

(i) What is the probability that the card is the queen?

(ii) If, the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?

**Solution:**

**(i)**

There are five cards.

Let E be the event that card drawn is queen.

Total number of outcomes favorable to event E=1 (Because there is just 1 queen)

Total number of possible outcomes=5 (We have 5 cards)

P(E)=(Total number of possible outcomes favorable to event E)/Total number of possible outcomes=1/5

**(ii)**

Queen has already been drawn and put aside. Therefore, we now have just 4 cards left.

**(a)**

Let A be the event that card drawn is an ace.

Total number of outcomes favorable to Event A=1 (We have 1 ace out of 4 cards)

Total number of possible outcomes=4 (We have 4 cards left)

P(A)=(Total number of outcomes favorable to event A)/(Total number of possible outcomes)=1/4

**(b) **

Let B be the event that card drawn is queen.

Total number of outcomes favorable to Event B=0 (We have no queen left in 4 cards.)

Total number of possible outcomes=4 (We have 4 cards left)

P(B)=(Total number of outcomes favorable to event B)/(Total number of possible outcomes)=0/4=0