Five cards-ten, jack, queen, king, and an ace of diamonds are shuffled face downwards. One card is picked at random. If a king is drawn first and put aside, what is the probability that the second card picked up is the (i) ace? (ii) king?

Given:

Five cards-ten, jack, queen, king, and an ace of diamonds are shuffled face downwards. One card is picked at random. A king is drawn first and put aside.

To do:

We have to find the probability that the second card picked up is the (i) ace? (ii) king

Solution:

A king 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 king $=0$

Total number of favourable outcomes $=0$.

Therefore,

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

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

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Updated on: 10-Oct-2022

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