Richard has just been given a 8-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all eight questions, find the indicated probabilities. (Round your answers to three decimal places.) a)What is the probability that he will answer all questions correctly? b)What is the probability that he will answer all questions incorrectly? (c) What is the probability that he will answer at least one of the questions correctly? Compute this probability two ways. First, use the rule for mutually exclusive events and the probabilities shown in the binomial probability distribution table.   answer: __________   Then use the fact that P(r ≥ 1) = 1 − P(r = 0).   answer: __________

John is having a dinner at a restaurant, which sells 3 kinds of dishes, A, B, and C. The probabilities of ordering each dish are 0.4, 0.3, and 0.3. Suppose the probability of John being satisfied after eating the dishes are 0.7, 0.5, and 0.6, respectively. Answer the questions below. 1) When John wasn’t satisfied with his dish, what is the probability that he has eaten the dish B? (Round an answer to two decimal places.)   2) What is the probability that John satisfies after eating the dish?

Jeri is listening to the songs on a new CD in random order.  She will listen to two different songs, and will buy the CD if she likes both of them.  Assume that there are 10 songs on the CD and that she would like 5 of them. Before she had listened to any of the songs on the CD, what would have been the probability that she would buy the CD?  Hint:  To find this probability, first find the number of combinations of 2 out of the 5 songs that she likes (how many different combinations of 2 out of the 5 songs are there?).  Then find the number of combinations of 2 out of the 10 songs on the CD (how many different combinations of 2 songs can she pick from the CD?).  Take the number of combinations of the 5 songs she likes and divide that by the number of combinations of the 10 songs..      Question 7 options:   A. 10/45 or 22% B. 10/120 or 8.3% C. 4/9 or 44% D. 45/10 or 450%

You order sixteen burritos to go from a Mexican restaurant, nine with hot peppers and seven without. However, the restaurant forgot to label them. If you pick four burritos at random, find the probability of the given event. (Round your answer to three decimal places.) Exactly one has hot peppers.

Kim is playing scrabble. What is the probability she chooses the tiles with the letters of her name, in order, when she draws three tiles from the bag? (Assume that when she begins there is one tile of each letter in the alphabet.