Question

Amar keeps picking playing cards out of a standard deck of 52 cards in the hopes that he will

draw a spade. There are 13 spades in the deck. After looking at each card, he places it back in
the deck. What is the probability that Amar will draw a spade in the first five attempts?
O 24%
O45%
076%
O 81%

Answer 1

The required probability is, 0.78

Explanation:

There are, (52 - 13) = 39 cards which are not spade

5 cards can be chosen from the deck of 52 cards in

`^(52){C}_(5)` ways

and out of these 5 choices, none of them will be spade in,

`^(39){C}_(5)` ways

So,

P(None of the chosen cards is spade)

=
`\frac {^(39){C}_(5)}{^(52){C}_(5)}`

`\simeq 0.22`

Hence,

P(out of these 5 choices, at least one card is spade)

`\simeq (1 - 0.22)`

= 0.78