1. An experiment looks at each of 20 cards with a circle, star, wave, or a square. They have a 0.25 probability of guessing what is correctly on each card.

1. Is this a binomial distribution? Explain your answer
2. What is the probability of exactly 5 correct guesses?
3. What is the probability that less than 7 cards were guessed correctly?

2) A believer in the "random walk" theory of stock markets thinks that an index of stock prices has a probability of 0.65 of increasing in any year. Assume the change in the index is not influenced by previous years. Let x be the number of years among the next 6 years in which the index rises.

1. Describe the binomial distribution.

b) What are the possible values that X can take?

c) Find the probability that the stock increased in exactly 4 years.

3) A federal report finds that lie detector tests given to truthful persons have a probability of 0.2 of suggesting the person is being deceptive.

1. A company asks 12 job applicants about thefts from previous employers, using a lie detector to assess their truthfulness. What is the probability that the lie detector says that all 12 are truthful?
2. What is the probability that the lie detector says at least one is deceptive?