Question

In a binomial experiment the probability of success is 0.06. what is the probability of two successes in seven trials? 0.0600 0.0555 0.0866 0.0036

Answer 1

Fill in the values into the base equation;

p(X=x)=(nCr)(0.06)ˣ(0.94)⁽ⁿ⁻ˣ⁾

Where n is the number of trials, x is the probability of success, p is probability of success and q is the probability of failure.

X~B(7, 0.06)

P(X=2)=(7C2)(0.06)²(0.94)⁵
P(X=2)=0.05548

Double check by inputting into a scientific calculator;

P(X=2)=0.05548 ≈ 0.0555

Hope I helped :)

Answer 2

Answer: 0.0555

Explanation:

Binomial probability formula to find the probability of getting success in x trials out of n trials is given by :-

`P(x)=^nC_xp^x(1-p)^(n-x)`, here p is the probability of getting success in each trial.

Given : In a binomial experiment the probability of success is 0.06.

Then, the probability of two successes in seven trials will be :-

`P(x)=^7C_2(0.06)^2(1-0.06)^(7-2)\\\\=(7!)/(2!(7-2)!)(0.06)^2(0.94)^5\\\\=0.0554831440934approx0.0555`