Question

Five cards- 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?

Answer 1

i) Total number of cards $n\left(S\right)=5$

Let $Q\equiv$ Event that queen of diamonds is drawn.

$\therefore n\left(Q\right)=1$

So, $P\left(Q\right)=\frac{n\left(Q\right)}{n\left(S\right)}=\frac{1}{5}$

ii)

a) If the queen is put aside, then the total number of cards $n\left(S\right)=4$

Let $A\equiv$ Event that ace of diamonds is drawn.

$\therefore n\left(A\right)=1$

So, $P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{1}{4}$

b) If the queen is put aside, then the total number of cards $n\left(S\right)=4$

Let $B\equiv$ Event that queen of diamonds is drawn.

$\therefore n\left(B\right)=0$ ...Since the queen was already put aside.

So, $P\left(B\right)=\frac{n\left(B\right)}{n\left(S\right)}=0$