To attract shoppers, a supermarket runs a weekly contest that involves “scratch-off” cards. With each purchase, customers get a card with a black spot obscuring a message. When the spot is scratched away, most of the cards simply say, “Sorry—please try again.” But during the week, 100 customers will get cards that make them eligible for a drawing for free groceries. Ten of the cards say they may be worth $\$ 200,10$ others say $\$ 100,20$ may be worth $\$ 50,$ and the rest could be worth $\$ 20 .$ To register those cards, customers write their names A technology store holds a contest to attract shoppers. Once an hour, someone at checkout is chosen at random to play in the contest. Here’s how it works: An ace and four other cards are shuffled and placed face down on a table. The customer gets to turn over cards one at a time, looking for the ace. The person wins $\$ 100$ of store credit if the ace is the first card, $\$ 50$ if it is the second card, and $\$ 20, \$ 10,$ or $\$ 5$ if it is the third, fourth, or last card chosen. What is the average dollar amount of store credit given away in the contest? Estimate with a simulation. on them and put them in a barrel at the front of the store. At the end of the week the store manager draws cards at random, awarding the lucky customers free groceries in the amount specified on their card. The drawings continue until the store has given away more than $\$ 500$ of free groceries. Estimate the average number of winners each week.

## Discussion

## Video Transcript

No transcript available

## Recommended Questions

Universal blood donors People with type O-negative blood are universal donors. That is, any patient can

receive a transfusion of O-negative blood. Only 7.2% of the American population have O-negative blood. If 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor? Follow the four-step process.

People with O-negative blood type are universal donors, i.e. they can donate blood to individuals with any blood type. Only $8 \%$ of people have O-negative.

a) One person randomly appears to give blood. What is the probability that hel she does not have O-negative?

b) Two people appear independently to give blood. What is the probability that

(i) both have O-negative?

(ii) at least one of them has O-negative?

(iii) only one of them has O-negative?

c) Eight people appear randomly to give blood. What is the probability that at least one of them has O-negative?

United Blood Services is a blood bank that serves more than 500 hospitals in 18 states. According to their website, a person with type O blood and a negative Rh factor (Rh-) can donate blood to any person with any bloodtype. Their data show that 43% of people have type O blood and 15% of people have Rh- factor; 52% of people have type O or Rh- factor.

a. Find the probability that a person has both type O blood and the Rh- factor.

b. Find the probability that a person does NOT have both type O blood and the Rh- factor.

About 40% of the blood donors at a local facility give O-positive blood. In a typical hour the facility will process twenty donors. Tell how to simulate an experiment to determine how many of those 20 donor hours in a 9-hour day will result in fewer than 4 donors with O-positive blood.

A couple has two children. One child has blood type A, and the other child has blood type O. What are all the possible blood types of the parents?

(A) Either both have type A, or one has type A and the other has type $\mathrm{O},$ or one has type $\mathrm{A}$ and the other has type $\mathrm{B}$ .

(B) There is only one possibility. Both parents have type A blood.

(C) There is only one possibility. Both parents have type $\mathrm{O}$ blood.

(D) There is only one possibility. One parent has type A, and the other has type O.

(E) It is not possible to determine from the information given.

Blood types All human blood can be typed as one of O, A, B, or AB, but the distribution of the types varies

a bit with race. Here is the distribution of the blood type of a randomly chosen black American:

(a) What is the probability of type AB blood? Why?

(b) What is the probability that the person chosen does not have type AB blood?

(c) Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that a randomly chosen black American can donate blood to Maria?