At a soccer (aka football) game, the probability of a goal keeper saving from a penalty kick is 0.3. After facing five different penalty kicks, assuming each penalty kick is independent, what is the probability that the goal keeper saves exactly three of the penalty kicks

50% of the senior class is female. Of the females, 20% are school athletes. What is the probability that a senior selected at random is a female school athlete?

Joe decided to spend his day fishing. He knows that the probability that a single cast will be a success and catch a fish is 0.10 and the probability of a successful cast stays constant no matter how many times he casts. a. If he casts 10 times, what is the probability that he will catch exactly 1 fish? b. What is the probability of catching his first fish on the 10th cast? c. What is the probability of catching exactly 2 fish from 10 casts? d. What is the probability of catching his second fish on the 10th cast? e. The probability distribution used for a. is which case below: Bernoulli, Binomial, Geometric, Negative Geometric, Hypergeometric, Poisson, Uniform, Normal, Multinomial or something not in this list f. The probability distribution used for b. is which case above? g. The probability distribution used for c. is which case above? h. The probability distribution used for d. is which case above?

In a large population, 68 % of the people have been vaccinated. If 4 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated? Give your answer as a decimal (to at least 3 places) or fraction.