Answer:
B. 0.00467
Explanation:
This is a binomial probability problem. The probability of fewer than three adults watching prime-time TV live is the sum of the probabilities of 0, 1, and 2 adults watching prime-time TV live.
Let X be the number of adults watching prime-time TV live. The probability mass function of X is given by:
P(X=k)=(kn)p^k(1−p)^n−k
where n is the number of trials (7 in this case), k is the number of successes, and p is the probability of success on a single trial (0.8 in this case).
So, the probability that fewer than three of the selected adults watch prime-time TV live is:
P(X<3) = P(X=0) + P(X=1) + P(X=2)
=(7 0)(0.8)^0(0.2)^7 + (7 1)(0.8)^1(0.2)^6 + (7 2)(0.8)^2(0.2)^5
=1/78125 + 28/78125 + 336/78125
=73/15625
=0.004672