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Long hair is a recessive trait for cats. One-third of "Desert Lynx" domestic cats are born with long hair. What is the probability that in a litter of five Desert Lynx kittens, exactly two will have long hair?

a) 0.333

b) 0.312

c) 0.329

d) 0.423

Respuesta :

reinhard10158

Answer:

c)

Step-by-step explanation:

the probability for a cat to have long hair/fur is 1/3.

the probability for 2 cats is then

1/3 × 1/3 = 1/9

the probability for a cat to have short hair/ fur is 1-1/3 = 2/3.

the probability for 3 cats is then

2/3×2/3×2/3 = 8/27

the probability for exactly one constellation of 2 cats out of 5 to have long hair is

1/9 × 8/27 = 8/243

now, how many options do we have to "pick" 2 out of 5 ?

there are no repetitions. and the sequence does not matter, so we use combinations

C(5, 2) = 5! / ((5-2)! × 2!) = 5! / (3! × 2) = 5×4/2 = 10

so, the total probability for 2 cats out of 5 having long hair/ fur is

10×8/243 = 80/243 = 0.329218107...

so, c) is the right answer.

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