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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
Solution
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 |
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