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?

Given:

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

To do:

We have to find

(i) the probability that the card is the queen.

(ii) the probability that the second card picked up is

(a) an ace

(b) a queen

when the queen is drawn and put aside

Solution:

Total number of cards $=5$

This implies,

The total number of possible outcomes $n=5$.

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

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 of getting the queen $=\frac{1}{5}$

The probability of getting the queen is $\frac{1}{5}$.      

(ii) 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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