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suppose x is a binomial random variable with parameters n and p given below. compute the indicated probability in each of these cases. a) If n=4n=4 and p=0.4p=0.4 then P(X=0)=P(X=0)= . b) If n=4n=4 and p=0.1p=0.1 then P(X=4)=P(X=4)= . c) If n=5n=5 and p=0.1p=0.1 then P(X=0)=P(X=0)= . d) If n=3n=3 and p=0.3p=0.3 then P(X=0)=P(X=0)=



Answer :

The probability of each of these cases when binomial random variable with parameters n and p are given:

a. 0.4116, b. 0.5625, c. 0.329, d. 0.375, e. 0.0046

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The formula is,

P(x)=(n/x)(P)ˣ(1-P)ⁿ⁻ˣ

a. n=4, x=1, p=0.3

P(x)=0.4116

b. n=2, x=0, p=0.25

P(x)=0.5625

c. n=5, x=2, p=0.33

P(x)=0.329

d. n=4, x=2, p=0.5

P(x)=0.375

e. n=3, x=3, p=1/6

P(x)=0.0046

When a binomial random variable with parameters n and p is given, the probability of each of the following cases is given is: a. 0.4116, b. 0.5625, c. 0.329, d. 0.375, and e. 0.0046

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