Question

1. A pro basketball player is a poor​ free-throw shooter. Consider situations in which he shoots a pair of free throws. The probability that he makes the first free throw is 0.51. Given that he makes the​ first, suppose the probability that he makes the second is 0.64. Given that he misses the​ first, suppose the probability that he makes the second one is 0.36.

What is the Probability he makes both free throws?

2. The most likely scenario for an accident for a natural gas pipeline is​ natural-gas leakage from a hole in the pipeline. The probability that the leak ignites immediately​ (I) causing a jet fire is .03. If the leak does not immediately​ ignite, it may result in the delayed ignition​ (D) of a gas cloud. If there is no delayed​ ignition, the gas cloud will disperse harmlessly​ (H). Given no immediate​ ignition, the probability of delayed ignition causing a flash fire is .03. Suppose a leak occurs in the​ natural-gas pipeline.

The probability that either a jet fire or a flash fire will occur is?

3. Red snapper is a rare and expensive reef fish served at upscale restaurants. A certain law prohibits restaurants from serving a​ cheaper, look-alike variety of fish​ (vermilion snapper or lane​ snapper) to customers who order red snapper. Researchers at a university used DNA analysis to examine fish specimens labeled​ "red snapper" that were purchased form vendors across the country. The DNA tests revealed that 78​% of the specimens were not red​ snapper, but the​ cheaper, look-alike variety of fish.

Assuming that the results of the DNA analysis are​ valid, what is the probability that you are actually served red snapper the next time you order it at a​ restaurant?

The probability is?

Answer 1