Question

In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials?

Answer 1

Answer:

Step-by-step explanation:

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

Answer 2

Answer:

0.055

Step-by-step explanation:

Probability of success = 0.06

Probability of failing = 1 - 0.06 = 0.94

Probability of 2 successes in 7 trials

= ⁷C2 × (0.06)² × (0.94)⁵

= 7!/(2! ×5!) × (0.06)² × (0.94)⁵

~ 21 × 0.0026

= 0.055