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A high school student is anxiously waiting to receive mail
Chapter 3, Problem 52P(choose chapter or problem)
A high school student is anxiously waiting to receive mail telling her whether she has been accepted to a certain college. She estimates that the conditional probabilities of receiving notification on each day of next week, given that she is accepted and that she is rejected, are as follows:
\(\begin{array}{lcc}
\hline \text { Day } & P(\text { mail|accepted }) & P(\text { mail|rejected }) \\
\hline \text { Monday } & .15 & .05 \\
\text { Tuesday } & .20 & .10 \\
\text { Wednesday } & .25 & .10 \\
\text { Thursday } & .15 & .15 \\
\text { Friday } & .10 & .20 \\
\hline
\end{array}\)
She estimates that her probability of being accepted is .6.
(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?
Questions & Answers
QUESTION:
A high school student is anxiously waiting to receive mail telling her whether she has been accepted to a certain college. She estimates that the conditional probabilities of receiving notification on each day of next week, given that she is accepted and that she is rejected, are as follows:
\(\begin{array}{lcc}
\hline \text { Day } & P(\text { mail|accepted }) & P(\text { mail|rejected }) \\
\hline \text { Monday } & .15 & .05 \\
\text { Tuesday } & .20 & .10 \\
\text { Wednesday } & .25 & .10 \\
\text { Thursday } & .15 & .15 \\
\text { Friday } & .10 & .20 \\
\hline
\end{array}\)
She estimates that her probability of being accepted is .6.
(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?
ANSWER:Step 1 of 6
Let us define events as,
M = mail to come by monday,
T = mail to come by tuesday,
W = mail to come by wednesday,
Th = mail to come by thursday, and
F = mail to come by friday.
Also we have:
|
Day |
P(mail|accepted) |
P(mail|rejected) |
|
Monday |
0.15 |
0.05 |
|
Tuesday |
0.2 |
0.1 |
|
Wednesday |
0.25 |
0.1 |
|
Thursday |
0.15 |
0.15 |
|
Friday |
0.1 |
0.2 |
Where, The probability of accepted is 0.6.
Here our goal is:
a). We need to find the probability that she receives mail on Monday.
b). We need to find the conditional probability that she receives mail on Tuesday given that she does not receive mail on Monday.
c). We need to find the conditional probability that she will be accepted.
d). We need to find the conditional probability that she will be accepted if mail comes on Thursday.
e). We need to find the conditional probability that she will be accepted if no mail arrives that week.