Question

A deck of playing cards contains 52 cards, half of which are red cards. What is the probability that the deal of a five-card hand provides:

1) No red cards?

2) At least 3 red cards?

a) .325, .025

b) .325, .5

c) .5, .325

d) .025, .50

e) .5, .15

Answer 1

(1)

Number of Red cards = 26

Number of Non-red cads = 26

Total number of cards = 52

Number of cards selected = 5

Number of ways of selecting 5 cards from 52 cards =

Number of ways of selecting 5 Non-red cards from 26 Non-red cards =

So,

P(No Red cards) = 65780/2598960 = 0.025

(2)

Number of ways of selecting 5 cards from 52 cards =

Number of ways of selecting 3 Red cards from 26 Red cards =

Number of ways of selecting 2 Non-Red cards from 26 Non-Red cards =

So,

P(3 Red cards) = 2600 X 325/2598960 = 0.3251

Number of ways of selecting 4 Red cards from 26 Red cards =

Number of ways of selecting 1 Non-Red cards from 26 Non-Red cards =26

P(4 Red cards) = 14960 X 26/2598960 = 0.1497

Number of ways of selecting 5 Red cards from 26 Red cards =

So,

P(5 Red cards) = 65780/2598960 = 0.0253

So,

P(At least 3 Red cards) = 0.3251 + 0.1497+ 0.0253 = 0.50

So,

Correct option:

(d) .025, .50