Question

Five cards- ten, jack, queen, king, and an ace of diamonds are shuffled face downwards. One card is picked at random.
(i) What is the probability that the card is a queen.
(ii) 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.

Answer 1

Total no. of cards given $=5$

Solution(i):

No. of queen $=1$

Therefore, ${}^1{C}_1$( Selecting $1$ out of $1$ items) times out of ${}^5{C}_1$( Selecting $1$ out of $5$ items) a queen is picked.

Let $E$ be the event of getting a queen from given cards

We know that, Probability $P\left(E\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{{}^1{C}_1}{{}^5{C}_1}$$=\frac{1}{5}$

Solution(ii):

From the given $5$ cards, a king is drawn and put aside.

Total no. of cards given $=4$

(i) -

No. of ace cards $=1$

Therefore, ${}^1{C}_1$( Selecting $1$ out of $1$ items) times out of ${}^4{C}_1$( Selecting $1$ out of $4$ items) an ace card is picked.

Let $E$ be the event of getting an ace card from given cards

We know that, Probability $P\left(E\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{{}^1{C}_1}{{}^4{C}_1}$$=\frac{1}{4}$

(ii ) -

Since the king is kept aside, there is no king left out. Hence the event of picking a king cannot happen. Therefore,

Probability, $P\left(king\right)=0$