A high school student is anxiously waiting to receive mail telling her whether she has been accepted to a certain college. On Sunday, she estimates the conditional probabilities of receiving notification on each day of upcoming week, given that she is accepted and that she is rejected, are as follows: Day P(mail|accepted) P(mail|rejected)
Monday .15 .05
Tuesday .20 .10
Wednesday .25 .10
Thursday .15 .15
Friday .10 .20
A) What is the probability that she receives mail on Monday?
B) What is the conditional probability that she receives mail on Tuesday given that she does not receive mail on Monday?
C) If there is no mail through Wednesday, what is the conditional probability that she will be accepted?
D) What is the conditional probability that she will be accepted if mail comes on Thursday?
E) What is the conditional probability that she will be accepted if no mail arrives that week?

35-60 students are taking math.

1/3 + 1/3 ≠ 2/6 because 1/3 alone = 2/6  

step by step explanation:

1/3 + 1/3 = 2/3       2/3=4/6

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt