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# IF A PENNY IS TOSSED FOUR TIMES AND COMES UP HEADS ALL FOUR TIMES, THE PROBABILITY

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Author: Christine Farr
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Quiz 31. If a penny is tossed four times and comes up heads all four times, the probabilitya. 0b. 1/32c. 0.5d. larger than the probability of tailse. None of the above2. Two events are mutually exclusivea. if their intersection is 1b. if they have no sample points in commonc. if their intersection is 0.5d. both a and c are correcte. None of the above3. Given that event E has a probability of 0.25, the probability of the complement oa. cannot be determined with the above informationb. can have any value between zero and onec. must be 0.75d. is 0.25e. None of the above4. Of five letters (A,B,C,D, and E), two letters are to be selected at random. How maa. 20b. 7c. 5!d. 10e. 225. If A and B are independent events with P(A) = 0.5 and P(B) = 0.3, then P(AUB) =6. Using #5 P(A l B) =? (A GIVEN B)7. Using #5 If A and B are mutually exclusive, P(A INTERSECT B) = ?8. Using #5 If A and B are mutually exclusive, P(AUB)=?9. A lottery uses 4 urns containing chips 0 to 9. One chip is selected at random from10. A die is tossed twice. What is the probability of obtaining 6 dots both times? 11. If P(A) = 0.3 and P(AUB) = .88 and P(A intersect B) = .12, then P(B)= ?***********************************************************************************Remember P(AUB) = P(A) +P(B) - P(A intersect B)P(A l B) = P(A intersect B)/P(B)Independent Events: P(A intersect B) = P(A)*P(B)P(A) = 1 - P(A**C) where A**C means complement of AA fair coin is tossed 4 times.1. How many outcomes are there in the sample space? (5 pts)2. What is the probability that the third toss is heads, given that thefirst toss is heads? (10 pts)3. Let A be the event that the first toss is heads, and B be the eventthat the third toss is heads. Are A and B independent? Why or why not?There are 1000 juniors in a college. Among the 1000 juniors,200 students are taking STAT200, and 100 students are takingPSYC300. There are 50 students taking both courses.4.What is the probability that a a randomly selected junior istaking at least one of these two courses5.What is the probability that a a randomly selected junior istaking PSYC300, given that he/she is taking STAT200?

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