Question

This exercise assumes familiarity with counting arguments and probability.

Kent's Tents has four red tents and three green tents in stock. Karin selects four of them at random. Let X be the number of red tents she selects. Give the probability distribution. (Enter your probabilities as fractions.)

x	1	2	3	4
P(X = x)

Find

P(X ≥ 2).

(Enter your probability as a fraction.)

P(X ≥ 2) =

Answer 1

Number of ways in which r items can be selected from n available items, nCr = n!/(r! x (n-r)!

Total number of tents = 4 + 3 = 7

Number of ways in which 4 tents can be selected from the 7 tents = 7C4

= 7!/(3! x 4!)

= 35

P(selecting 1 red tent) = P(selecting 1 red tent from 4 and 3 green tents from 3)/Total number of selections possible

= 4C1 x 3C3 / 35

= 4 x 1 /35

= 4/35

P(selecting 2 red tents) = P(selecting 2 red tents from 4 and 2 green tents from 3)/Total number of selections possible

= 4C2 x 3C2 / 15C4

= 6 x 3 / 35

= 18/35

P(selecting 3 red tents) = P(selecting 3 red tents from 4 and 1 green tent from 3)/Total number of selections possible

= 4C3 x 3C1 / 15C4

= 4 x 3 /35

= 12/35

P(selecting 4 red tents) = P(selecting 4 red tent from 4 and 0 green tents from 3)/Total number of selections possible

= 4C4 x 3C0 / 15C4

= 1 x 1 /35

= 1/35

X	1	2	3	4
P(X = x)	4/35	18/35	12/35	1/35

P(X 2) = 18/35 + 12/35 + 1/35

= 31/35