Algebra II Wilsen BLOCK 5 Unit 10: Probability Day Nine

Transcription

1 Algebra II Wilsen BLOCK 5 Unit 10: Probability Day Nine Example 1 Elizatalie and Merethan visit the Children s Ward at the hospital. Elizatalie has a 13% chance of catching mumps as a result of the visit, and Merethan has a 7% chance. Fill out a sample space for this situation, and then find the probabilities asked for below. Sample Space: (all boxes should add to ) P (Elizatalie gets mumps) P (Elizatalie doesn t get mumps) P (Merethan gets mumps) P (Merethan doesn t get mumps) a) they both catch mumps b) Elizatalie does not catch mumps c) Merethan does not catch mumps d) At least one catches mumps e) Neither catches mumps

2 Binomial Probabilities The conditions for a binomial probability are as follows: There are only two outcomes ( success or failure ); There is the same probability (p) of success in each trial; The outcome of each trial is independent from the next. Tremi has a weighted coin that has a 60% chance of coming up heads. He flips it 5 times. Not caring about order, only considering the total number of heads and tails that come up, what are all the possibilities and associated probabilities? Event 5 heads 0 tails 4 heads 1 tail 3 heads 2 tails 2 heads 3 tails 1 head 4 tails 0 heads 5 tails Number of different ways Probability of 1 such way Number of ways probability of 1 way NOTE: This is the expansion of the binomial ( ) 5 = 5C 0 ( 0.6) 5 ( 0.1) C 1 ( 0.6) 4 ( 0.1) + 5 C 2 ( 0.6) 3 ( 0.1) C 3 ( 0.6) 2 ( 0.1) C 4 ( 0.6) 1 ( 0.1) C 5 ( 0.6) 0 ( 0.1) 5 = P(5H) + P(4H 1T) + P(3H 2T) + P(2H3T) + P(1H 4T) + P(5H)

3 1. Ms. Wilsen is taking tests in math and history next week. For math, her probability of getting an A is 0.15, a B is.80, and a C is For history, her probability of getting an A is 0.25, a B is 0.65 and a C is Fill out the sample space and find the probabilities asked for below. a) she gets 2 A s b) she gets 2 B s or better c) she gets exactly 1 C 2. Two traffic lights on Massachusetts Avenue operate independently. Your probability of being stopped at the first one is 0.4 and the probability of being stopped at the second one is 0.7. What is your probability of being stopped at: a) both lights? b) neither light? c) the first but not the second? d) the second but not the first? e) exactly one of the lights? 3. Vital systems such as electric power distribution systems have backup components in case one component fails. Suppose that two generators each have a probability of 98% working. They system will continue to work as long as at least one of the generators works. What is the probability that the system will continue to operate?

4 4. Three basketball teams from LS each play on Friday night. The probabilities that they will win are: varsity 0.7, JV 0.6, and freshmen 0.8. What is the probability that a) all three win? b) all three lose? c) at least one team wins? d) the varsity team wins and the others lose? 5. Calvin Andhobbes has the following probabilities of passing various courses: sociology 90%, speech 80% and latin 95%. What is his probability of a) passing all three? b) failing all three? c) passing exactly 1? 6. If dark-haired mothers and fathers have a particular type of gene, they have a 0.25 probability of having a light-haired baby. a) What is their probability of having a dark-haired baby? b) If they have 3 babies, calculate their probabilities of having exactly 0, 1, 2 and 3 dark-haired babies. c) Show that your answers to part b are reasonable by finding the sum.

5 7. Clara Nett plays a musical solo. She is quite good, and figures that her probability of playing any one note right is 99%. The solo has 60 notes. (a) What is the probability of her getting every note right? making exactly one mistake? making exactly two mistakes? making at least two mistakes? b) What must be Clara s probability of getting any one note right if she wants to have a 95% probability of getting all 60 notes right? c) What is the probability that Clara will convey passion through her music, if she plays every note right? 8. The probability that Polly Gollywog scores on a free throw is 7. 9 If she takes 5 free throws, what is the probability of her missing 3 of them? 9. An article in USA Today reported that approximately 1 out of 6 cars sold in 1994 was green. Suppose a salesperson sells 7 cars one week. What is the probability that 3 of those are green?

6 10. Eight out of every ten nutritionists recommend Brand X. If nutritionist A, B and C are asked their opinion of Brand X, what is the probability that at least one recommends Brand X? 11. You had a quiz today consisting of four multiple choice questions with options of A, B, C, D or E, only one of which is correct. You stayed up late last night playing Mario Kart instead of studying (!), and so you had to guess on all four questions. Calculate the probabilities of your getting 0, 1, 2, 3 and 4 questions correct. You ll pass if you get 3 questions correct. What are the chances of THAT??