First slide

Theorems of probability

Question

While shuffling a pack of 52 playing cards, 2 are accidentally dropped. The probability of the two missing cards to be of different colours (colours may be taken as red and black) is

Easy

A

$\frac{15}{51}$
B

$\frac{1}{13 \times 51}$
C

$\frac{1}{26 \times 51}$
D

$\frac{26}{51}$

Solution

The number of ways of selecting two cards from 52 cards is    $n (S) = C (52, 2) = 26 \times 51$

Let E be the event of getting a red and black card
Hence,
$\begin{array}{rcl} n (E) & = & C (26, 1) \times C (26, 1) \\ = & 26 \times 26 \end{array}$
The probability of  the missing cards to be different colors is $P (E)$
$∴ P (E) = \frac{26 \times 26}{26 \times 51} = \frac{26}{51}$

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