Answer :
The probability that at least 2 babies out of a cluster of 5 babies will speak tomorrow is 47/128.
The probability that less than 2 babies will speak is
5C0 * (0.25)^0 * (0.75)^5 + 5C1 * (0.25)^1 * (0.75)^4
= (0.75)^5 + 5 * 0.25 * (0.75)^4
(0.75)^5+5*0.25*(0.75)^4 = 81/128
Therefore,
probability that 2 or more will speak is
= 1- 81/128 = 47/128
The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability p) or failure (with probability display style q=1-pq=1-p).
This distribution is used in probability theory and statistics. A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results.
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