Question

A light bulb manufacturing process results in 6% of the light

bulbs being defective. If 5 light bulbs are randomly
selected, find the probability that all of the light bulbs are
fully functioning.

Answer 1

`Probability = 0.734`

Explanation:

Given

Represent the event that a bulb is defective with p.

So:

`p =6\%`

Required

Determine the probability that all 5 are fully functioning

Represent the event that a bulb is defective with q.

So:

`p + q = 1`

Make q the subject

`q = 1 - p`

Substitute 6% for p

`q = 1 - 6\%`

Convert % to decimal

`q = 1 - 0.06`

`q = 0.94`

If 5 were selected and all are functioning, the event is represented as: q q q q q

And the probability is:

`Probability = q * q * q * q *q`

`Probability = q^5`

Substitute 0.94 for q

`Probability = 0.94^5`

`Probability = 0.7339040224`

`Probability = 0.734` --- approximated