a coin is tossed 5 times the probability of tails on any tos

a coin is tossed 5 times. the probability of tails on any toss is 0.43. let x denote the numberof tails that comes up

(a) what is probability of tails at most once?

(b) what is probability of tails more than 2 times but less than 5?

a coin is tossed 5 times. the probability of tails on any toss is 0.43. let x denote the numberof tails that comes up

(a) what is probability of tails at most once?

This is binomial. Number of trials, n = 5. P = 0.43.

At most 1 tail is 0 tails or 1 tail.

The probability formula for the binomial distribution:

P(X = x) = nCx*p^(x)*(1-p)^(n-x)

P(X = 0) = 5C0*.43^0*(1-.43)^(5-0) = .060619

P(X = 1) = 5C1*.43^1*(1-.43)^(5-1) = .226954

P(X = 0 or 1) = .060619 + .226954 = .287123

Answer: 0.2871

(alternatively on a calculator with a binomcdf function: binomcdf(5, .43, 1) = 0.2871

(b) what is probability of tails more than 2 times but less than 5?

More than 2 but less than 5 is 3 or 4

P(X = 3) = 5C3*.43^3*(1-.43)^(5-3) = .258318

P(X = 4) = 5C4*.43^4*(1-.43)^(5-4) = .097436

P(X = 3 or 4) = .258318 + .097436 = .355754

Answer: 0.3558

(alternatively on a calculator with a binompdf function: binompdf(5, .43, 3) + binompdf(5, .43, 4) = 0.3558