A fair quarter is flipped three times. For each of the following probabilities,

Question

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.

Explanation / Answer

A quarter flipped three times

So here n = 3, p = probability of getting head or tail = 0.5

The Binomial distribution formula is

p ( X = x ) = nCx * px * ( 1 - p ) n-x  

a) Exactly three heads :

p ( X = 3) = 3C3 * 0.53 * ( 1 - 0.5 ) 3-3

= 0.125

b) Exactly two heads :

p ( X = 2) = 3C2 * 0.52 * ( 1 - 0.5 ) 3-2

= 0.375

c) p ( two or more heads ) = p ( x = 2) + p( x = 3) = 0.125 +0.375 = 0.500

d) Getting exaactly three tails

p ( y = 3 ) =  3C3 * 0.53 * ( 1 - 0.5 ) 3-3 = 0.125

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