ASSN 3: SUPPLEMENTARY (selected) PROBABILITY PROBLEMS 1. A class contains 50 members, including 18 Freshmen, 10 Sophomores, 8 Juniors and 14 Seniors. One student is selected at random from the class. We have 50 equiprobable outcomes. Four events are defined as follows: F = (selectee is a Freshman) , S = (selectee is a Sophomore), J = (selectee is a Junior), A = (selectee is a Senior). Calculate: C (i) P(F and J) C (j) P(F or S or J) (a) P(F) (e) P(A ) (b) P(S) (f) P(F ) (c) P(J) (g) P(F or A) (d) P(A) (h) C P(F and J) 2. Two marbles are drawn from a box containing several red, several yellow, and several green marbles. Give a sample space for this experiment. 4. A fair coin is tossed and either a head or a tail is observed. If a head is observed, the coin is tossed a second time. However, if a tail is observed, a fair die is rolled. Give the sample space for this experiment. What is the probability that a die is rolled in the second stage of this experiment? 5. A box in a warehouse contains 100 identical pieces of which 10 are defective and 90 are good. Three parts are chosen, without replacement, and are noted as either Good or Defective. Draw a tree diagram to show the sample space for this problem. 6. Three people are to be interviewed as to their attitude towards decentralization of the city school system, i.e., Pro, Con, or Undecided. Give the sample space. How many possible outcomes are there? 7. Two flower seeds are selected from a package that contains five seeds for red flowers and three seeds for white flowers. What is the probability that one seed of each color is selected? 8. A basket contains 2 white chips and 3 black chips. Two chips are chosen with replacement. Find the probability that at least one chip is white. 9. Three coins are tossed and the number of heads observed is recorded. Find the probability for each of the possible results: 0H, 1H, 2H, and 3H. 10. In each case a-d, determine whether the given pair of events, A and B, are mutually exclusive. a) Five coins are tossed. A: one head is observed, B: at least one head is observed. b) A salesperson calls on a client and makes a sale. A: the sale exceeds $100, B: the sale exceeds $1000. c) One student is selected at random from a student body. A: the person selected is male, B: the person selected is over 21 years of age. d) Two dice are rolled. A: the total value showing is less than 7, B: the total showing is more than 9. 11. There are eight students in a reading group. Three of the students are classified as strong readers, three as average and two as weak readers. A researcher wants to work with two randomly selected students from this group. What is the probability that both of the students she selects are the same type of reader? (copyright 1995-2004 by James E. Corter) 12. A newspaper vendor randomly mixes 50 late papers with 30 early editions. Two people come to buy a paper, one right after the other. Draw a tree diagram which represents all possible outcomes for the two newspaper sales. What is the probability that both customers receive late editions? 16. There are fifty seagulls on a beach. A researcher wishes to randomly tag two of the birds for her study. There are thirty-five brown seagulls and fifteen white ones. What is the probability that she tags one of each color? 24. If P(A)=.4, P(B)=.5, and P(A and B)=.25, find P(A or B). 25. If P(A)=.7, P(not B)=.4, and P(A and B)=.5, find P(A or B). (copyright 1995-2004 by James E. Corter)