Question

Calculate the probabilities of each of these situations. A standard deck of cards has 52 cards and 13 cards cards in each suit (Spades, Clubs, Hearts, & Diamonds). Which of the following is LEAST likely to occur? a) Selecting any spade card from a standard deck of cards, keeping it, then selecting the queen of hearts. b) Selecting a spade from a standard deck of cards, not putting it back, then selecting another spade. c) Selecting an ace from a standard deck of cards, not replacing it, then selecting a king.Event CEvent AEvent B

Answer 1

The least likely to occur is Event C

Step-by-step explanation

A.

P(spade card) = 13/52

P(queen) = 4/51 Note: Without replacement

⇒ 13/52 x 4/51

= 52/2652

= 0.0196

B.

P(a spade) = 13/52

P( another spade) = 12/51 Note: Without replacement

⇒ 13/52 x 12/51

= 156/2652

= 0.0588

C.

P(an ace) = 4/52

P(king) = 4/51

⇒ 4/52 x 4/51

= 16/2652

= 0.006

∴ The least likely to occur is Event C