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

Question

A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a jack or eight. (b) Compute the probability of randomly selecting a jack or eight or four. (c) Compute the probability of randomly selecting an ace or spade. a. P(jack or eight) = 0.1541 (Round to three decimal places as needed) b. P(jack or eight or four) = 0.231 (Round to three decimal places as needed.) c. P(ace or spade) = 0.308 (Round to three decimal places as needed.)

Explanation / Answer

a) P( jack or eight) = P(jack) + P(eight) - P(jack and eight)

= (4C1 / 52C1) +( 4C1 / 52C1) - 0

= (4 / 52) + (4 / 52)

= 0.154

B) P(jack or eight or four) = P(Jack) + P(eight) + P(four) - P(jack and eight) - P (eight and four) - P(four and jack) + P(jack and eight and four)

= (4 / 52) +( 4 / 52) + (4 / 52) - 0 - 0 - 0 + 0

= 0.231

C) P(ace or spade) = P(ace) + P(spade) - P(ace and spade)

= (4C1 / 52C1) + (13C1 / 52C1) -(1C1/52C1)

=( 4 / 52) + (13 / 52) - (1 / 52)

= 0.308

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