AliceGmaddie
Answered

7 females, and 5 males including Larry.

There are 4 tasks to be assigned. Note that assigning the same

people different tasks constitutes a different assignment.

(1) Find the probability that both males and females are given a task.

(2) Find the probability that Larry and at least one female

are given tasks.

Verified Answer :

meerkat18

1. Ways to choose Lar, 1F, 2 other M} = 1 C(7,1) C(4,2) = 42
Ways to choose {Lar, 2F, 1 other M}; = 1 C(7,2) C(4,1)= 84

Ways to choose {Lar, 3F, 0 other M} = 1 C(7,3) C(4,0) = 35

Ways to choose 4 from 12 is C(12,4) = 495

P(L and at least 1F) = [42 + 84 +35] / 495 = 161/495 =.325 approx


2. P(Larry and at least 1 F)
  P(at least 1F) = 1 - P(0F) = 1 -{ [C(7,0)C(5,4)] } / C(12,4) = 5/495 = 490/495 = 98/99 = .99.

 
Ways to choose Larry = 1 C(1,1) = 1

P(Larry and at least 1 F) = 1(98/99) = 98/99 = .99 approx

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