Two cards are drawn simultaneously at random from a well shuffled pack of 52 Cards. Let X be the random variable which denotes number of kings in the draw. Then the probability distribution of X is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) →
|
$X$ |
0 |
1 |
2 |
|
$P(X)$ |
$\frac{{^{48}C}_2}{{^{52}C}_2}$ |
$\frac{{^4C}_1×{^{48}C}_1}{{^{52}C}_2}$ |
$\frac{{^4C}_2}{{^{52}C}_2}$ |
Total ways to choose 2 cards from 52: ${}^{52}\!C_{2}$
Case 1: X = 0
Ways to choose 2 non-kings from 48: ${}^{48}\!C_{2}$
$P(X = 0) = \frac{{}^{48}\!C_{2}}{{}^{52}\!C_{2}}$
Case 2: X = 1
Ways to choose 1 king from 4 and 1 non-king from 48: ${}^{4}\!C_{1} \cdot {}^{48}\!C_{1}$
$P(X = 1) = \frac{{}^{4}\!C_{1} \cdot {}^{48}\!C_{1}}{{}^{52}\!C_{2}}$
Case 3: X = 2
Ways to choose 2 kings from 4: ${}^{4}\!C_{2}$
$P(X = 2) = \frac{{}^{4}\!C_{2}}{{}^{52}\!C_{2}}$