A fair quarter is flipped three times. For each of the following probabilities, use the formula for the binomial distribution and a calculator to compute the requested probability. Next, look up the probability in the binomial probability distribution table. (Enter your answers to three decimal places.)

(a) Find the probability of getting exactly three heads.

(b) Find the probability of getting exactly two heads.

(c) Find the probability of getting two or more heads.

(d) Find the probability of getting exactly three tails.

 

Answer:

A fair quarter is flipped three times. For each of the following probabilities, use the formula for the binomial distribution and a calculator to compute the requested probability. Next, look up the probability in the binomial probability distribution table. (Enter your answers to three decimal places.)

let random variable of getting a head be X , x = 0,1,2,3

probability of success, p = 1/2

probability of failure , q = 1/2

Binomial formula :

P(X = x) = n C x * ( p)^x * ( q)^{n - x} , n C x is read as (n combination x)

n = 3

(a) Find the probability of getting exactly three heads.

P( X = 3) = 3 C 3 * ( 1/2)³ * ( 1/2)^{3 - 3}

P( X = 3) = 0.125

(b) Find the probability of getting exactly two heads.

P( X = 2) = 3 C 2 * ( 1/2)² * ( 1/2)^{3 - 2}

P( X = 2) = 0.375

(c) Find the probability of getting two or more heads.

P( X >= 2) = P( X = 2) + P( X = 3)

= 0.375 + 0.125

= 0.50

(d) Find the probability of getting exactly three tails.

P( X = 0) = 3 C 0 * ( 1/2)⁰ * ( 1/2)^{3 - 0}

P( X = ) = 0.125