For any married couple who are members of a squash club, the probability that the husband has a degree is 2/4 and the probability that the wife has a degree is 1/4. The probability that the husband has a degree given that his wife has a degree is 3/9. A married couple is chosen at random.

a) show that the probability of them both having degrees is 3/36
b)Find the probability that only one of them has a degree.
c) Find the probability that neither of them has a degree.

A study was made of 413 children who were hospitalized as a result of motor vehicle crashes. Among 290 children who were not using seat belts, 50 were injured severely. Among children using seat belts, 16 were injured severely (based on data from “Morbidity Among Pediatric Motor Vehicle Crash Victims: The Effectiveness of Seat Belts,’’ by Osberg and Di Scala, American Journal of Public Health, Vol. 82, No. 3).

a) State the null hypothesis and alternative hypothesis.
b) Compute the test statistic.
c) Is there sufficient sample evidence to conclude, at the 0.05 significance level, that the rate of severe injuries is lower for children wearing seat belts?
d) Calculate the p-value.
e) State a conclusion about the null hypothesis and state a final conclusion that addresses the original claim

A study was made of 413 children who were hospitalized as a result of motor vehicle crashes. Among 290 children who were not using seat belts, 50 were injured severely. Among children using seat belts, 16 were injured severely (based on data from “Morbidity Among Pediatric Motor Vehicle Crash Victims: The Effectiveness of Seat Belts,’’ by Osberg and Di Scala, American Journal of Public Health, Vol. 82, No.

To answer these questions, we need to make use of conditional probability and the concept of joint probability. Let's go through each question step by step:

a) To find the probability that both the husband and wife have degrees (denoted as H and W respectively), we need to multiply the conditional probability of the husband having a degree given that the wife has a degree (P(H|W)) by the probability that the wife has a degree (P(W)). Mathematically, it can be written as:
P(H and W) = P(H|W) * P(W)

Given the values provided:
P(H|W) = 3/9
P(W) = 1/4

Plugging these values into the equation:
P(H and W) = (3/9) * (1/4)
= 3/36

Therefore, the probability that both the husband and wife have degrees is 3/36.

b) To find the probability that only one of them has a degree, we need to consider two cases: either the husband has a degree while the wife does not (H and not W) or the wife has a degree while the husband does not (not H and W).

P(H and not W) = P(H) * P(not W|H)
= (2/4) * (1 - 1/4)

Similarly,
P(not H and W) = P(not H) * P(W|not H)
= (2/4) * (1 - 3/4)

Adding these probabilities together gives:
P(only one has a degree) = P(H and not W) + P(not H and W)

You can calculate this using the numbers provided to find the final probability.

c) Finally, to find the probability that neither of them has a degree (not H and not W), we can subtract the sum of probabilities calculated above from 1, since the probabilities of all possible outcomes must sum to 1.

P(not H and not W) = 1 - [P(H and W) + P(H and not W) + P(not H and W)]

Again, substitute the appropriate probabilities into the equation and solve to find the final probability.

Hope this helps!