# Probability Assignments | Online Homework Help

1. You’re a physician. You think it is quite likely (80% probability) that one of your patients has strep
throat, but you aren’t sure. You take some swabs from the throat and send them to a lab for testing.
The test is not perfect: if the patient has strep throat, then 70% of the time the lab says YES. If the
patient does not have strep throat, then 90% of the time the lab says NO. You send 2 swabs to the
lab from the same patient. You get two NOs. What is the probability of this patient having strep
throat?
2. You are in charge of organizing a party held for the sole purpose of raising money for a worthy cause.
You must decide whether to schedule an outdoor picnic or an indoor buffet supper. There is a 1/3
chance of rain.

If it does not rain, the outdoor picnic will yield a profit of \$500, and the indoor buffet will
yield a profit of \$170.

If it rains, the outdoor picnic will yield a profit of \$80, and the indoor buffet will yield a profit
of \$440.

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3. A friend of yours, who has never taken a course in critical thinking, has been playing a game with a
stranger: they roll / flip a coin twice. If they get heads both times, the stranger gives your friend \$5;
if they get exactly one head, your friend gives the stranger \$3; if they get tails both times, your
friend gives the stranger \$2. With simple calculations, you realize your friend is losing money. How
much does your friend lose, on average, after 10 rounds?
4. There are two lotteries you can choose from, both cost \$5 to enter. You only have \$5 on you so you
can only choose one. Lottery A asks you to pick a card at random from a standard deck (52 cards)
and pays you \$50 if you get an ace. Lottery B asks you to flip a coin 4 times and pays you \$100 if you
get all heads. Which lottery is the better deal?
5. “Enter the Charity Lottery!
One Grand Prize of \$20,000
Tickets only \$10”
After reading the fine print, you discover that 10,000 tickets will be sold to this charity lottery. Is this
a good value for you (leaving aside its charitable purposes)?
6. Imagine a game as follows: it costs you \$10 to play. For each round, you are asked to draw 5 cards
out of a standard deck of cards (with replacement). If exactly 4 of those 5 are hearts, you win a
prize; otherwise, you lose. What would be an appropriate prize such that the game is fair? (Round to
nearest cent.)

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