First slide

Theorems of probability

Question

Two cards are drawn at random from a pack of 52 cards. The probability that one of them is black and other is red is

Easy

A

$\frac{13}{51}$
B

$\frac{26}{51}$
C

$\frac{13}{102}$
D

$\frac{13}{204}$

Solution

The number of ways of selecting 2 cards from 52 cards is
$\begin{array}{rcl} n (S) & = & C (52, 2) \\ = & \frac{52 \times 51}{2} \\ = & 26 \times 51 \end{array}$

Suppose E be the event of getting one red and one black cards from the pack of cards
$\begin{array}{rcl} n (E) & = & C (26, 1) \cdot C (26, 1) \\ = & 26 \cdot 26 \end{array}$
Therefore, the probability to the event E is $P (E) = \frac{26 \times 26}{26 \times 51} = \frac{26}{51}$

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