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

2 thoughts on “In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials?”

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

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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

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