Statistics Review Answers

NAME: Key no outcomes & & REVIEW PACKET one event In commen doesn't affect other event 1. Decide whether the following sets of 2 events are disjoint, independent, both, or neither? a. Rolling a dice and flipping a coin disjoint and independent b. (From a standard 52 card deck) Picking an Ace and picking a red card (with replacement in between each pick) not disjoint, but independent (there are red aces)' c. Rolling a 6 and rolling a 3 disjoint and indep. d. Rolling a 6' and rolling an even number not disjoint, but independent e. Flipping a coin, getting a HEAD and getting a TAIL disjoint independent 2. If P(A) = 0.6 and P(B) = 0.21 and P(A∩B) = 0.09, find the following: a. P(A cup B)=P(A)+P(B)-P(A cap B)=O; 6 + O * 0.2 * 1 - 0.09 = (0.72) b. P(B|A)= P(A cap B) P(A) = 0.09/0.6 =. overline 0.15 c. Are A and B disjoint events? Why or why not? no, P(ANB) #0 d. Are A and B independent? Why or why not? no, P(ANB) + P(A).P(B) 3. P(D) = 0.17 P(C) 0.54 and D and Care disjoint) what is the probability of D or C? P(D cup C)= P(D) + P(c) = 0.17 + 0.54 =(0.7i 4. If P(k) = 0.68 P(R) = 0.22 and K and R are independent, what is the probability of K and R? P(K cap R)= P(K) * P(R) = (0.68)(0.22) = sqrt(0.1496) 5. If P(F) = 0.51 and P(H) = 0.22 and P( H |F)=0.12, find the following: a. P(Fan * dH) = P(F ^ H) =P(F)* P(H|F)=(O.51)(O*12)=0.0612) b. P(ForH) = P(F,OH) =P(F)+P(H)-P(F cap H)=0,51+0.22- infty c. What is P(F)? I - P(F) = 1 - 0.51 = 0.49 0.6688 d. What is the complement of H? 1 - P(H) = 1 - 0.22 = 0.78 6. Let the sample space, S = 1 all whole number from 5 through 20) Let the event A = (5, 8, 10, 11, 14, 18, 19, 20) Let the event B = \{6, 8, 10, 12, 14, 16, 18, 20\} Let the event C = (5, 7, 9, 11, 13, 15, 17, 19) Find the following: a. A cap B=\ 8, 10, 14 ,i8,20\ b. P(A cap B)= 5 / rho c. s ^ c = \{5, 7, 9, 11, 13, 15, 17, 19\} d. P( B cap C)=10 e. P(A cap c)= 3 / i * b f. P(A ^ 6) = 8/16 g. CUB= 5,6,7,8,9,..., 18, 19, 20 \ For the next 2 questions, put the probability statements into notation to help you. 7. On a certain day, there is a 21% chance of John being absent. The probability of there being a pop quiz and John being absent is 15%. What is the probability that there is a pop quiz given that John is absent? P(A) = 0.21 P(Q cap A)= 0.1S P(Q|A)= 0.15/0.21 = 0.7143 8. The chance of Kelly wanting cereal for breakfast is 48%. The chance that Kelly has Milk in her fridge and her wanting cereal is 39%. What is the chance that Kelly has milk given that she wants cereal. P(c) = 0.48 P( M cap C)=0.39 P(M|C)= (P(mu ^ c))/(P(c)) = 0.39/0.48 > 0.8125 9. There are 30 books on a shelf. Jimmy wants to select 7 books to read this summer. How many groups of 7 can he select? 30nCr * 7 =203 5,800 10. License plates in NJ are made up of 2 letters followed by 4 digits followed by 1 letter. Letters cannot be repeated. How many different ways can we do this? 26 * 25 * 10 * 10 * 10 * 24 11. You are at a buffet and want to make a dinner platter for yourself with a main course, a side dish, a salad and a dessert. There are 10 choices for main dishes, 6 side dishes, 3 salads, and 5 desserts. How many different platters can you create? 10 * 6 * 3 * 5 = 900 12. The PTA wants to create a group of parents to advise the school on issues. They want 4 dads and 4 moms to be on the committee. There are 51 men and 70 women. How many possibilities are there? (5ln(r 4)*( 70n (r 4)=(2.291*10^ prime prime 13. On a typical 747 plane, there are 150 seats. The chance that the plane is completely filled is 56%. The chance that the plane has 120 seats filled is 24%. The chance that the plane has 70 seats filled is 12% and the chance that the plane has only 30 seats filled is 8%. a. Create a probability model for the number of passengers on the plane 150 120 70 30 P(x) 0.56 0.24/0.12/0.08 b. What is the expected attendance.on.a.747 flight? F(x)= 123.6 people c. What is the chance that less than 100 seats will be filled? 0.12+0.08 0.20 = 20%. d. What is the chance that more than 70 seats are filled? 0.56+0.24 = 0.80 = 80% e. If there are 50 flights in a day, what is the total expected attendance? 50 x 123.6=6180 people Book: p.475 #24-26 24 E(x)=3 25 x12 E (x) = 3.5 3 4 5 6 26 a) 1-(0.5+0.42+0.05) = (0.03 b) don't do!