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There are 20 students in a club, 12 boys and 8 girls. If five members of the club are chosen at random to represent the club at a competition, what is the probability that in the group chosen there are exactly 2 boys? Explain why this is not a Bernoulli experiment.

In \(3-5,\) find exact probabilities showing all required computation. Five fair coins are tossed. Find the probability of the coins showing: \(\begin{array}{ll}{\text { a. at least four heads }} & {\text { b. at least three heads }} \\ {\text { c. at least two heads }} & {\text { d. at least one head }}\end{array}\)

A spinner is divided into five equal sections numbered 1 through \(5 .\) The arrow is equally likely to land on any section. Find the probability of: a. an odd number on any one spin b. at least three odd numbers on four spins c. at least two odd numbers on four spins d. at least one odd number on four spins

In \(3-6,\) find exact probabilities showing all required computation. A multiple-choice test of 10 questions has 4 choices for each question. Only one choice is correct. A student who did not study for the test guesses at each answer. a. What is the probability that that student will have exactly 5 correct answers? b. What is the probability that that student will have only 1 correct answer?

Two cards are drawn from a standard deck of 52 cards without replacement. What is the probability that both cards are kings?

State whether the events are independent or dependent. Tossing a coin and rolling a die

In \(10-13,\) the mean and standard deviation of a normal distribution are given. Find each probability to the nearest hundredth. mean \(=8,\) standard deviation \(=1, P(7 \leq x)\)

State whether the events are independent or dependent. Picking 2 cards from a standard deck without replacing the first card

A die was rolled \(1,200\) times and a 5 came up 429 times. a. Find the experimental probability for rolling a \(5 .\) b. Based on a comparison of the experimental and theoretical probabilities, do you think the die is fair? Explain your answer.

In \(14-17\) , use the normal approximation to estimate each probability. Round your answers to three decimal places. . \(P(\text { at most } 100 \text { successes }), p=\frac{6}{7}, n=125\)