Two cards are drawn simultaneously from a well shuffled pack of 52 cards. If X is the random variable of getting queens, then the value of 2 E(X)+3 E (X^2 ) for the number of queens is

Step-by-step solution

Let X be the random variable denoting the number of queens drawn when selecting two cards from a standard 52-card deck. There are 4 queens and 48 non-queens. The total number of ways to choose 2 cards is 52 2 = 52 51 2 = 1326 . X takes values 0, 1, or 2. The probability of drawing 0 queens is the number of ways to choose 2 non-queens divided by the total: P(X=0) = 48 2 1326 = 1128 1326 = 188 221 . For exactly one queen, the favorable outcomes are 4 1 48 1 = 4 48 = 192 , so P(X=1) = 192 1326 = 32 221 . For two queen