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

Given:

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.

The queen is drawn and put aside.

To do:

We have to find the probability that the second card picked up is (i) an ace (ii) a queen.

Solution:

A queen is drawn and put aside.

This implies,

Total number of remaining cards $=4$

The total number of possible outcomes $n=4$.

(i) Number of cards that are ace $=1$

Total number of favourable outcomes $=1$.

We know that,

Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

Therefore,

Probability that the second card picked up is the ace $=\frac{1}{4}$

(ii) Number of cards that are queen $=0$

Total number of favourable outcomes $=0$.

Therefore,

Probability that the second card picked up is a queen $=\frac{0}{4}=0$

The probability that the second card picked up are the ace and the queen are $\frac{1}{4}$ and $0$ respectively.       

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Updated on: 10-Oct-2022

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