practice test finite math problem please help?

Question

19. Jack wants to buy a two-scoop sundae at Baskin-Robbins. How many choices of flavor combinations
(C) does he have if he is allowed to choose the same flavor twice? Recall that there are 31 flavors in all!
(Chocolate and Vanilla is the same as Vanilla and Chocolate.)

(a) P(31, 2) (b) C(31, 2) (c) C(31, 2) + 31 (d) P(31, 2) + 31 (e) 312 (f) none of the others

I said A because you are selecting and arranging the flavors. The correct answer is C. Please someone explain

20. For two events A and B we are given that Pr[A] = 1/3, Pr[B|A] = 1/2, and Pr[B|A] = 1/5. Find
Pr[B]. (A)
(a) 3/10 (b) 7/10 (c) 7/20 (d) 1/2 (e) 2/5 (f) none of the others

this question the answer is A, i had no idea how to figure this one out

for question number 20 it should be andr[B|A]== 1/5 it is a' complement

Answer 1

You are counting possible outcomes.

The answer is C because you can choose C(31, 2) xombinations of 2 flavors. However since you can choose the same flavor twice, you have another 31 possibilities, a possibility for each flavor.

Therefore, the correct answer is C. You have C(31, 2) + 31 possible flavor combinations.

For #20, you mst have copied the problem wrong. You have written P(B|A) twice, once at 1/2 and once at 1/5. Give us the correct problem and we'll look at it for you.

Answer 2

For 20, you mistyped. You said p(B|A) = 1/2 and then you said p(B|A) = 1/5. One of those should probably been p(A|B). Otherwise you have a contradition.

For 19, picture a times table from 1 to 31. On the main diagonal you have 1x1, 2x2, and so on. Above the main diagonal you have 1x3, 3x5, and so on. Below the main diagonal you have 3x1, 5x3, and so on, which duplicates the top half except for order. You have C(31,2) entries above the main diagonal, C(31,2) below, and 31 entries ON the diagonal. If you didn't allow same flavor twice, your C(31,2) would have been right, but since you do, you add the 31 pairs of same flavor that are on the diagonal.

Answer 3

19. because you have 31 choices and 2 can be the same when your writing posibilities you use parantheses.

20. you had all the numerators together, then u add all the denominators and you get your fraction 3/10.