Answer to Question #164329 in Statistics and Probability for Mariana Morales Zuleta

Question

a standard deck of cards contains 52 cards. One card is selected from the deck.

​(a)

Compute the probability of randomly selecting a seven or three.

​(b)

Compute the probability of randomly selecting a seven or three or jack.

​(c)

Compute the probability of randomly selecting a nine or diamond

Answer 1

(a) P(seven or three) = P(seven) + P(three)

$= \frac{4}{52} + \frac{4}{52} \\ = \frac{8}{52} \\ = \frac{2}{13} \\ = 0.154$

(b) P(seven or three or jack) = P(seven) + P(three) + P(jack)

$= \frac{4}{52} + \frac{4}{52} + \frac{4}{52} \\ = \frac{12}{52} \\ = \frac{3}{13} \\ = 0.230$

(c) P(nine or diamond) = P(nine) + P(diamond) – P(nine $\cap$ diamond)

$= \frac{4}{52} + \frac{13}{52} - \frac{1}{52} \\ = \frac{4}{13} \\ = 0.307$