Dugi asked in Science & MathematicsMathematics · 3 years ago

# Probability math question?

Update:

Suppose that 8% of the first batch of computer chips off a new production line have flaws. An inspector randomly selects 5 computer chips for testing.

a) Create a probability histogram for the number of flawed computer chips in the sample.

b) What is the expected number of flawed computer chips in the sample?

Relevance
• 3 years ago

Use the binomial probability formula:

P(X = k) = C(n,k) * p^k * q^(n-k)

n : number of trials (5)

k : number of desired outcomes (0, 1, 2, ..., 5)

p : probability of that outcome (0.08)

q : probability of the opposite outcome (1-p = 0.92)

Now just create a probability histogram.

P(X=0) = C(5,0) * 0.08^0 * 0.92^5 = 0.6590815232

P(X=1) = C(5,1) * 0.08^1 * 0.92^4 = 0.286557184

P(X=2) = C(5,2) * 0.08^2 * 0.92^3 = 0.049836032

P(X=3) = C(5,3) * 0.08^3 * 0.92^2 = ...

P(X=4) = C(5,4) * 0.08^4 * 0.92^1 = ...

P(X=5) = C(5,5) * 0.08^5 * 0.92^0 = ...

For the expected number of chips, compute the Expected Value.

E(X) = 0 * P(X=0) + 1 * P(X=1) + 2 * P(X=2) + 3 * P(X=3) + 4 * P(X=4) + 5 * P(X=5)