There are 24 people. 9 have black hair, 4 have brown hair, 5 have blonde hair,...

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Question

There are 24 people. 9 have black hair, 4 have brown hair, 5 have blonde hair,...

There are 24 people. 9 have black hair, 4 have brown hair, 5 have blonde hair, and 6 have red hair. 3 people are then selected at random without replacement.

Solve the following probabilities:

(a) What is the probability that all 3 people selected have red hair.

(b) What is the probability that 2 people selected have the same color hair color, and the other person selected has a different hair color

math Statistics-And-Probability

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Answer 1

Answer #1

Total = 24

Black hair = 9 , Brown Hair = 4 , Blonde Hair = 5 , Red Hair = 6

a) P(All 3 red ) = ⁶ C ₃ / ²⁴ C ₃

= 20/2024

= 5/506

= 0.0099

b) P( 2 with same color ) = {P(2 black)*22 +P(2 brown)*22 + P(2 Red)*22 +P(2 blonde)*22} / ²⁴ C ₃

= 22(⁹ C ₂ + ⁴ C ₂+ ⁵ C ₂ + ⁶ C ₂ )/ ²⁴ C ₃

= 22(36+6+10+15)/2024

= 0.7283

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Answer 2

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