Question

A single card is drawb from a standard 52-card deck. What is the probability that the card is either

a) a seven, or an eight, or a ten?

b) a heart, or a club, or a spade?

c) a five, or an ace, or a heart?

d) a queen, or an eight, or a club, or a spade?

Answer 1

Answer)

Probability is = (favorable)/(total)

Total = 52

A)

Favorable = seven or eight or ten

There are 4 sevens and 4 eights and 4 tens in a standard deck of a card

Required favorable here is 4+4+4 = 12

Required probability is = 12/52 = 0.2307692307692

B)

Favorable = heart or club or spade

There are 13 hearts and 13 clubs and 13 spades

Favorable = 13+13+13 = 39

Required probability = 39/52

= 0.75

C)

Favorable = five or ace or heart

There are 4 fives and 4 ace and 13 hearts

But we need to subtract 2 from the sum, to eliminate the double counting of heart ace and 5 of heart.

= 4+4+13-2

= 19

Required probability = 19/52 = 0.3653846153846

D)

Favorable = queen or eight or club or spade

There are 4 queens and 4 eights and 13 clubs and 13 spades.

But we need to subtract 4 from the sum to eliminate double counting

Favorable = 4 + 4 + 13 + 13 - 4 = 30

Required probability = 30/52 = 0.5769230769230