Question

In a pack of 52 playing cards, two cards are drawn at random simultaneously. If the number of black cards drawn is a random variable, find the values of the random variable and number of points in its inverse images

Answer 1

Total number of playing cards = 52

Number of Black cards = 26

Number of Non-black or Red cards = 26

Let ‘X’ be the random variable denotes the number of black cards. Since two black cards are drawn, ’X’ takes the values 0, 1, 2

X(Non-black Cards) = X(26C₁ × 25C₁) = X(650) = 0

X(1 Black Card) = X(26C₁ × 26C₀) = X(26) = 1

X(2 Black Cards) = X(26C₁ × 25C₁) = X(650) = 2

Values of X	0	1	2	Total
Number of elements in inverse images	650	26	650	1326