Question

The soccer​ team's shirts have arrived in a big​ box, and people just start grabbing​ them, looking for the right size. The box contains 6 medium, 11 ​large, and 10 ​extra-large shirts. A player wants a medium for himself and one for his sister. Find the probability of each event described. Complete parts a through d below.

a) The first two you grab are the wrong sizes. b) The first medium shirt you find is the third one you check. c) The first four shirts you pick are all extra-large. d) At least one of the first four shirts you check is a medium. ​(Round to three decimal places as​ needed.)

Answer 1

Answer:

a)

Given,

P(first two you grab are the wrong sizes) = (21/27)*(20/26)

= 0.5983

b)

P(The first medium shirt you find is the third one you check) = (20/27)*(21/26)*(6/25)

= 0.1436

c)

P(The first four shirts you pick are all extra-large) = 10/27 * 9/26 * 8/25 * 7/24

= 0.01197

d)

P(At least one of the first four shirts you check is a medium) = 1 - P(None of the 1st 4 are medium)

= 1 - [(21/27)*(20/26)*(19/25)*(18/24)]

= 1 - 0.3410

= 0.6590