Question

# A boy has his allowance determined every Sunday by drawing one paper bill from an urn...

A boy has his allowance determined every Sunday by drawing one paper bill from an urn containing 5 bills in

total: three \$1 bills, one \$5 bill, and one \$10 bill.
\$1 \$1 \$1 \$5 \$10.

His parents refill the urn every week, so the content of the urn stays the same every week.

(a) (4pts) Let A be the event that the student draws the ten-dollar bill this Sunday, and B be the event that the student draws the ten-dollar bill the next Sunday.
(i) Are the events A and B disjoint?
(ii) Are the events A and B independent? Explain.

(b) (2pts) What is the probability that the boy draws a one-dollar bill for 5 consecutive weeks?

(c) (3pts) What is the probability that the boy gets a ten-dollar bill at least once in 5 consecutive weeks?

Stat 22000 Page 7

(d) (3pts) What is the expected amount of allowance the boy gets in a week?

(e) (3pts) What is the standard deviation of the amount of allowance the boy gets in a week?

(f) (5pts) What is the expected value of the amount of allowance that the boy can get in a year? And with what standard deviation? Assume a year has 52 weeks.