Question

a manufacturer tests 4 different light bulbs from a production line. the probability that a single bulb is defective is 0.06. what is the probability that all 4 tested light bulbs are defective? p(all defective) = (round to 6 decimal places for long decimal answers).

Explanation:

Step1: Identify probability of single - bulb defect

The probability that a single light bulb is defective is $p = 0.06$.

Step2: Use multiplication rule for independent events

Since the tests of different light bulbs are independent events, the probability that all $n = 4$ light bulbs are defective is given by the formula $P(X)=p^n$. Substitute $p = 0.06$ and $n = 4$ into the formula: $P(\text{All Defective})=(0.06)^4$.

Step3: Calculate the result

$(0.06)^4=0.06\times0.06\times0.06\times0.06 = 0.0001296\approx0.000130$.

Answer:

$0.000130$