probability of exactly

The region contains exactly one point, the point is optimal soluti..

Binomial Distribution - A trial, which has only two outcomes i.e., "a success" or "a failure", is called a Bernoulli trial. Let X be the number of successes in a Bernoulli trial, then X can take 0 or 1 and P(X =1) = p = "probability of a success" P(X = 0) = 1 - p = q = "probability..

If two events E 1 and E 2 can occur independently in exactly m ways and n ways respectively, then either of the two events can occur in (m + n) way..

The same principle can be generalized to three or more events occurring in succession as follows: If n operations can be performed in m 1 ,m 2 ,m 3 ,...m n ways respectively, then all n operations in succession can be performed exactly in m 1 ,m 2 ,m 3 ,...m n ways. The above principle..

The fundamental principle of counting (F.P.C) states that if an operation can be performed in m different ways and if for each such choice, another operation can be performed in n different ways, then both operations, in succession can be performed in exactly mn different ways. The prin..

A survey found that 55% of the families in the locality had a pet. If 20 families are selected at random, then find the probability that exactly 15 of them have a pet. => 0.75 or 0.55 or 0.41 or 0.037..

75% of the students in a class pass an examination. If 15 people are selected at random, then find the probability that exactly 7 of them have passed the examination. => 0.35 or 0.013 or 0.47 or 0.75..

A dice is thrown 6 times. If 'getting an even number' is a success, then what is the probability of exactly 5 successes? => 5 32 or 3 32 or 1 16 or 1 10..

In a town, 60% of the people support team A. If 5 people are selected at random, then find the probability that exactly 2 of these people support team A. => 0.02 or 0.23 or 0.6 or 0.4..

In a survey, it was found that 20% of the people smoke more than 3 packs of cigarettes a day. If 8 people are selected at random, then find the probability that exactly 5 people smoke more than 3 packs. => 0.009 or 0.2 or 0.09 or 0.125..