Homework # 8 - MATH 2227
The problems on this homework must be done alone. The honor code is in effect.
First name: Last name:
For questions 1-5, we roll a pair of fair dice: a red one and a white one. It's important that we can tell these dice apart. So getting a 1 on the red die and 2 on the white die is different than getting a 2 on the red die and 1 on the white die.
1. If we draw two cards from a well-shuffled deck without replacement, what is the probability that they are both hearts?
a. \(\frac{1}{16}\)
b. \(\frac{1}{17}\)
c. \(\frac{1}{18}\)
d. \(\frac{1}{20}\)
d. \(\frac{1}{24}\)
2. If we draw a card from a well-shuffled deck, put it back, reshuffle, and draw another card, what is the probability that both cards are hearts?
3. If the probability that it rains on a particular day is 30\(\%\), and the probability that my favorite bagel store is out of sesame seed bagels is 20\(\%\), then what is the probability that it rains AND the bagels store is out of sesame seed bagels (assume that these two events are independent)?
a. \(5\%\)
b. \(6\%\)
c. \(25\%\)
d. \(44\%\)
d. \(50\%\)
4. If the probability that it rains on a particular day is 30\(\%\), and the probability that my favorite bagel store is out of sesame seed bagels is 20\(\%\), then what is the probability that it rains OR the bagels store is out of sesame seed bagels (assume that these two events are independent)?