College Algebra Probability Extra Credit

For each question, you must explain your answer clearly in complete sentences to receive credit.

1. Four students decide to be absent for the final exam so they have more time to study. All four students come in together several hours after the final has ended and tell the professor they were late because the car they were driving in had a flat tire.

The professor says they can still take the final exam and puts each student in a separate room. The students cannot communicate with one another in any way. The professor puts only one question on the final and it’s worth 100 points. The question is “Which tire went flat?”

What is the probability that all four students guess the same tire? Also explain your answer.

2. There are 10 scratch-off circles on a game card. Each card can be a winning card, but you must scratch off the correct three circles that each reveal the prize symbol. You can scratch only three circles. If you scratch any of the seven non-winning circles, you automatically lose. What is the probability of scratching off the correct three circles? Also explain your answer.

3. Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1 [but the door is not opened], and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?”

What is your probability of winning the car if you keep your original choice of door #1?

What is your probability of winning the car if you switch your choice to door #2?