Question Detail
There is a pack of 52 cards and Rohan draws two cards together, what is the probability that one is spade and one is heart ?
- 11/102
- 13/102
- 11/104
- 11/102
Answer: Option B
Explanation:
Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:
Let sample space be S
\begin{aligned}
\text{then, n(S) = }^{52} C _2 \\
=> \frac{52 \times 51}{ 2 \times 1} = 1326 \\
\text {let E be event of getting 1 spade and 1 heart} \\
\text{So, n(E) = ways of getting 1 spade or 1 heart out of 13} \\
= ^{13}C_1 \times ^{13}C_1 \\
= 13 \times 13 \\
= 169 \\
\text{So, p(E) = }\frac{n(E)}{n(S)} \\
= \frac{169}{1326} = \frac{13}{102}
\end{aligned}