Question

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.
$\left(i\right)$ What is the probability that the card is jack?
$\left(ii\right)$ If the king is drawn and put aside, what is the probability that the second card picked up is $\left(a\right)$a queen and $\left(b\right)$a ten?

• A. $\left(i\right)\frac{1}{7}\left(ii\right)\left(a\right)\frac{1}{6},\left(b\right)\frac{1}{2}$
• B. $\left(i\right)\frac{1}{6}\left(ii\right)\left(a\right)\frac{1}{6},\left(b\right)\frac{1}{3}$
• C. $\left(i\right)\frac{1}{5}\left(ii\right)\left(a\right)\frac{1}{4},\left(b\right)\frac{1}{4}$
• D. $\left(i\right)\frac{1}{4}\left(ii\right)\left(a\right)\frac{1}{4},\left(b\right)\frac{1}{3}$

Answer 1

Answer: (C)

$\left(i\right)\frac{1}{5}\left(ii\right)\left(a\right)\frac{1}{4},\left(b\right)\frac{1}{4}$

(1) Here, Total cards$=5$
No. of jack$=1$
Hence, the no. of favorable outcomes$=1$
$\therefore$ probability = $\frac{1}{5}$
(2) If the king of diamond is drawn then remaining cards $=4$
(a) No. of queen$=1$
Hence, the no. of favorable outcomes$=1$
$\therefore$ probability = $\frac{1}{4}$
(b) No. of ten$=1$
Hence, the no. of favorable outcomes$=1$
$\therefore$ probability = $\frac{1}{4}$