In a baseball game, Tommy gets a hit 30% of the time when facing this pitcher. J
ID: 3206821 • Letter: I
Question
In a baseball game, Tommy gets a hit 30% of the time when facing this pitcher. Joey gets a hit 25% of the time. They are both coming up to bat this inning.
a. What is the probability that Joey or Tommy will get a hit?
b. What is the probability that neither player gets a hit?
c. What is the probability that they both get a hit?
2- An unfair coin has a probability of coming up heads of 0.65. The coin is flipped 50 times. What is the probability it will come up heads 25 or fewer times? (Give answer to at least 3 decimal places).
You draw two cards from a deck, what is the probability that:
a. both of them are face cards (king, queen, or jack)?
b. you draw two cards from a deck and both of them are hearts?
4- True/False: You are more likely to get a pattern of HTHHHTHTTH than HHHHHHHHTT when you flip a coin 10 times.
5- True/False: Suppose that at your regular physical exam you test positive for a relatively rare disease. You will need to start taking medicine if you have the disease, so you ask your doc- tor about the accuracy of the test. It turns out that the test is 98% accurate. The probability that you have Disease X is therefore 0.98 and the probability that you do not have it is .02. Explain your answer.
Explanation / Answer
Answer to question# 1)
P(tommy) = 0.30
P(joe) = 0.25
Since they both cannot be hit together simultaneously
P(tommy and Joe) = 0
.
Answer to part a)
P(tommy or Joey) = P(tommy) + P(joey)
P(tommy or joey) = 0.30 + 0.25 = 0.55
.
Answer to part b)
P(none) = 1 - P(tommy or Joey)
P(none) = 1 - 0.55 = 0.45
P(neither gets hit) = P(none) = 0.45
.
Answer to part c)
The probability that they both get hit together is Zero