Question

Consider a factory making nails. The probability of any nail being too thin is 0.15. If a chosen nail is too thin, then there is a 0.20 probability that the nail is also too short. What is the probability that a nail chosen at random is both too slim and too short?

O 0.03
O 0.75
O 0.20
O 0.80

Answer 1

Option 1. The probability that a nail chosen at random is both too slim and too short is 0.03, or 3%.

Step-by-step explanation:

The student is asking about the probability that a nail chosen at random from a factory is both too thin and too short. To find this probability, we need to use the concept of conditional probability where we multiply the probability of the first event by the probability of the second event, given the first event has already occurred.

Given that the probability of a nail being too thin is 0.15, and if a nail is too thin, there is a 0.20 probability that it is also too short, we calculate the probability of both occurring by multiplying these two probabilities, which is:

Probability(too thin) × Probability(too short | too thin) = 0.15 × 0.20 = 0.03

Thus, the probability that a nail is both too thin and too short is 0.03, which equates to 3%.