Probability Problem: Bolts and Nuts Selection

How to calculate the probability of selecting bolts or rusted bolts from a box containing 100 bolts and 50 nuts?

Given that 50% of the bolts and 50% of the nuts are rusted, two objects are selected from the box at random. What is the probability that both objects are bolts or bolts are rusted?

Probability Calculation

The probability that both objects are bolts or bolts are rusted is 0.375.

In this problem, we have a box containing 100 bolts and 50 nuts, with 50% of the bolts and nuts being rusted. To calculate the probability of selecting both bolts or rusted bolts, we need to consider two cases:

Initially, there are 100 bolts out of 150 objects in the box. The probability of selecting a bolt on the first draw is 100/150. After that, there are 99 bolts left in the box, so the probability of selecting another bolt on the second draw is 99/149. Therefore, the probability of both objects being bolts is (100/150) * (99/149).

Since 50% of the bolts are rusted, the probability of selecting a rusted bolt on the first draw is 0.5 * (100/150). After that, there are 99 rusted bolts left, so the probability of selecting another rusted bolt on the second draw is 0.5 * 99/149. Therefore, the probability of both objects being rusted bolts is (0.5 * 100/150) * (0.5 * 99/149).

The total probability is calculated by adding the probabilities of these two cases:

Total Probability = (100/150) * (99/149) + (0.5 * 100/150) * (0.5 * 99/149) = 0.375