Solve each of the following problems. 1. A coin is tossed four times. What is the probability that at least 2 heads will occur? 2. A pair of dice is rolled. What is the probability that the sum is equal to the following? a. 5 b. 10 c. at most 9 d. at least 8 3. A chip is drawn at random from a jar containing 8 red, 2 blue, 3 green, 4 yellow, and 3 white chips. Determine the probability that it is: a. Red b. Yellow or red c. Not orange 4. In a graduating class of 300 students, 162 studied Mathematics, 185 studied English, and 105 studied both Mathematics and English. If one of these students is selected at random for an interview, find the probability that: a. the student takes Mathematics or English; b. the student does not take either of these subjects; c. the student takes Mathematics but not English. 5. Among the 400 inmates of a prison, some are first offenders, some are hardened criminals, some serve terms of less than five years, and some serve longer terms, with the exact being Type of Criminals Terms of less than Five years Longer Terms First Offenders 120 40 Hardened Criminals 80 160 If one of the inmates is to be selected at random to be interviewed about prison conditions, H is the event that he is a hardened criminal, and L is the event that he is serving a longer term, determine each of the following probabilities: a. P(H) b. P(L) c. P(L∩H) d. P(L’∩H) e. P(L|H) f. P(H’ |L) 6. Let Z be a random variable for the number of heads obtained in four flips of a balanced coin. Construct a probability distribution table. 7. A basketball player has a history of making 80% of the foul shots taken during games. What Is the probability that of the five foul shots he a. Makes three missed shots b. Makes at least 3 shots c. Makes at most 2 shots 8. The 10 year survival rate for bladder cancer is approximately 50%. If 20 people who have bladder cancer are properly treated for the disease, what is the probability that? a. At least 1 will survive

Solve each of the following problems. 1. A coin is tossed four times. What is the probability that at least 2 heads will occur? 2. A pair of dice is rolled. What is the probability that the sum is equal to the following? a. 5 b. 10 c. at most 9 d. at least 8 3. A chip is drawn at random from a jar containing 8 red, 2 blue, 3 green, 4 yellow, and 3 white chips. Determine the probability that it is: a. Red b. Yellow or red c. Not orange 4. In a graduating class of 300 students, 162 studied Mathematics, 185 studied English, and 105 studied both Mathematics and English. If one of these students is selected at random for an interview, find the probability that: a. the student takes Mathematics or English; b. the student does not take either of these subjects; c. the student takes Mathematics but not English. 5. Among the 400 inmates of a prison, some are first offenders, some are hardened criminals, some serve terms of less than five years, and some serve longer terms, with the exact being Type of Criminals Terms of less than Five years Longer Terms First Offenders 120 40 Hardened Criminals 80 160 If one of the inmates is to be selected at random to be interviewed about prison conditions, H is the event that he is a hardened criminal, and L is the event that he is serving a longer term, determine each of the following probabilities: a. P(H) b. P(L) c. P(L∩H) d. P(L’∩H) e. P(L|H) f. P(H’ |L) 6. Let Z be a random variable for the number of heads obtained in four flips of a balanced coin. Construct a probability distribution table. 7. A basketball player has a history of making 80% of the foul shots taken during games. What Is the probability that of the five foul shots he a. Makes three missed shots b. Makes at least 3 shots c. Makes at most 2 shots 8. The 10 year survival rate for bladder cancer is approximately 50%. If 20 people who have bladder cancer are properly treated for the disease, what is the probability that? a. At least 1 will survive