One card is selected at random from an ordinary deck of 52 playing cards. Events

Question

One card is selected at random from an ordinary deck of 52 playing cards. Events A, B, and C are defined below. Find the probabilities for parts (a) through (h) below and express your results in words. Compute the conditional probabilities directly; do not use the conditional probability rule. Note that the ace has the highest value A = event a card higher than 9 is selected Bevent a card between 7 and 10, inclusive, is selected C event a spade is selected a. Find P(B). Express your result in words The probability that (Type an integer or a fraction. Simplify your answer.) b. Find P(BIA). Express your result in words. The probability that (Type an integer or a fraction. Simplify your answer.) c. Find P(BIC). Express your result in words. The probability that (Type an integer or a fraction. Simplify your answer.) d. Find P(BI(not A)). Express your result in words The probability that (Type an integer or a fraction. Simplify your answer.) is selected is selected, given that I selected is selected, given that I selected is selected, given that I selected is

Explanation / Answer

a) probability that a card between 7 and 10 is selected is 4/13 (as thses are 4 rank out of 13)

b) the probability that a card between 7 and 10 is selected given that a card higher than 9 is selected is 1/5

c) the probability that a card between 7 and 10 is selected given that a spade is selected is 4/13

d) probability that a card between 7 and 10 is selected given that a card higher than 9 is not selected =4/8 =1/2

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