Answers
(a)
Binomial Distribution:
n = Number of trials = 100
p = Probability of success in a single trial = p
So,
q = 1 - p
So,
Answer is:
(b)
Expected Number = n p = 100 p
So,
Answer is:
100 p
(c)
P(X
3) = 1 - [P(X =0) + P(X = 1) + P(X = 2)]
So
Binomial Distribution: n = Number of trials = 100 p = Probability of success in a single trial = p So, q = 1 - p P(X = 10) = (100 0) times (1 - p)^90 times p^10 = 1.7310 times 10^13 times (1 - p)^90 times p^10 so, 1.7310 times 10^13 times (1 - p)^90 times p^10 Expected Number = n p = 100 p So, 100 p p(x greaterthanorequalto 3) = 1 - [p(x = 0) + p(x = 1) + p(x = 2)] p(X = 0) = (100 0) times (1 - p)^100 times p^0 = 1 times (1 - p)^100 times 1 = (1 - p)^100 P(X = 1) = (100 1) times (1 - p)^99 times p^1 = 100 times (1 - p)^99 times p = 100(1 - p)^99 p P(X = 2) = (100 2) times (1 - p)^98 times p^2 = 4950 times (1 - p)^98 times p^2 = 4950(1 - p)^98 p^2 so P(X greaterthanorequalto 3) = 1 - [1
.
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