Question

Five cards the ten, jack, queen and aces of diamond, are well shuffled with their face down. One card is then picked up at random.

(i) What is the probability that the card is 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

Answer 1

Step 1. Determining the probability of getting Queen

Total number of cards $=5$

Total number of queen cards $=1$

$$\begin{gathered} P\left(E\right)=\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}} \\ =\frac{1}{5} \end{gathered}$$

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

Step 2. Determining the probability of getting Ace

Total number of cards $=4\left[\because \mathrm{Queen}\mathrm{is}\mathrm{not}\mathrm{in}\mathrm{the}\mathrm{sample}\right]$

Total number of Ace cards $=1$

$$\begin{gathered} P\left(E\right)=\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}} \\ =\frac{1}{4} \end{gathered}$$

Therefore the probability of getting Ace is $\frac{1}{4}$

Step 3. Determining the probability of getting Queen

Total number of Ace cards $=0[\because \mathrm{Queen}\mathrm{is}\mathrm{not}\mathrm{in}\mathrm{the}\mathrm{sample}]$

$$\begin{gathered} P\left(E\right)=\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}} \\ =0 \end{gathered}$$

Therefore the probability of getting queen is $0$

Hence, the probability of getting

(i) the card is queen is $\frac{1}{5}$

(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is

(a) An ace $\frac{1}{4}$

(b) A queen $0$