Dsing the same sssuple from problen #10 on the previousD KNOw tht a Dinosaur Cra

Question

Dsing the same sssuple from problen #10 on the previousD KNOw tht a Dinosaur Crane en person in the ile (A) ,18 given 02 12. A certain computer pasword in with po 5 gymabols kong, with no "special" characters, so it ia composed of just lower-case letters "a to a" and digits D to 9. If repeats are in how many Endr of im,-nd best, third bast? (She only ranks the top 3 stations, a wana li teaa to the radaon the web She Natam to 10 stations, but she hau her fin" rites cf courts mps could she raak bert not all 10 stations) hnln l 14. You pay $10 to roll one die. If the die is a "Hour" then you win $40. Let z be your net result. Find the expected value and the standard deviation of s. Hint: fill in the probabilities for the probability distribution below. win: z=$30 ker z =-$10 ra Credit (2 points each; do on back; no partial credit) You have two dice: one red and one blue. The red die is typical with 1 to 6 on its sides, but the blue die has zero on three si and has a one on the other three sides. If you roll the dice, find the probability that the sum is "five" f you flip a Tair coin 4 times, find the probablity that all 4 are heads, GIVEN THAT at least 3 are heads. Hint: th ONDITIONAL probability, so the answer is NOT equal to 1/16

Explanation / Answer

13) 3 stations can be chosen from 10 in 10C3 = 120 ways.
3 stations can be arrange in 3! = 6 ways.
Total possible combination = 120*6 = 720 ways

14) P(x= $30) = P(die is 4) = 1/6
P(x= -$10) = P(die is not 4) = 1-1/6 = 5/6
Expected value E(x) = (30*1/6) + ((-10)*5/6) = -$3.33
E(x^2) = (30^2 * 1/6) + (10^2 * 5/6) = 233.33
Var(x) = E(x^2) - [E(x)]^2 = 233.33 - 3.33^2 = 222.24
SD = sqrt(Var) = 14.9

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