3. Roll a fair die 10 times. Call a number in 1, 2, 3, 4, 5,...

Question

Question

3. Roll a fair die 10 times. Call a number in 1, 2, 3, 4, 5, 6 a loner if it is rolled exactly once on the 10 rolls.

(For example, if the rolls are 1 5 6 4 4 4 6 2 4 1, then 5 and 2 are the only loners)

a. Compute the probability that at leas tone of numbers 1, 2, 3 is a loner.

Answer 1

Answer #1

Answer:

Given,

sample = 10

p = 1/6

q = 1 - p = 1 - 1/6 = 5/6

let us consider,

x = 10C1*(1/6)*(5/6)^9

P(At least one of numbers 1,2,3 is a loner) = P(1) + P(2) + P(3) - P(1)*P(2) - P(1)P(3) - P(2)P(3) + P(1)P(2)P(3)

= 3x - 3x^2 + x^3

= 3(10C1*(1/6)*(5/6)^9) - 3(10C1*(1/6)*(5/6)^9)^2 + (10C1*(1/6)*(5/6)^9)^3

= 0.6897

Answer 2

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