4. Based on a certain survey, there is a 0.8 probability that a randomly selecte

Question

4. Based on a certain survey, there is a 0.8 probability that a randomly selected adult will watch prime-time TV live, instead of online, on DVR, etc. Assume that 5 adults are randomly selected, find the following:

a. The probability that exactly one of the selected adults watch prime-time TV live

b. The probability that none of the selected adults watch prime-time TV live   

c. The probability that at most two of the selected adults watch prime-time TV live   

d. The probability that at least two of the selected adults watch prime-time TV live

STEP BY STEP WITHOUT USING EXCEL

Explanation / Answer

p = 0.8

n = 5

P(X = x) = 5Cx * 0.8x * (1 - 0.8)5-x

A) P(X = 1) = 5C1 * 0.81 * 0.24 = 0.0064

B) P(X = 0) = 5C0 * 0.80 * 0.25 = 0.00032

C) P(X < 2) = P(X = 0) + P(X = 1) + P(X = 2)

= 5C0 * 0.80 * 0.25 + 5C1 * 0.81 * 0.24 + 5C2 * 0.82 * 0.23

= 0.0579

D) P(X > 2) = 1 - (P(X = 0) + P(X = 1))

= 1 - (0.0064 + 0.0003)

= 0.9933

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