# 7 Basic Probability Problems

1. A certain coin has the same probability of landing heads as it does landing tails - but this coin is special, because it also has a 30% chance of landing on its side.

a. What is the probability of this coin landing heads?

b. What are the odds against this coin landing on its side?

c. If this coin is tossed twice, what is the probability of it landing on its side both times?

d. If this coin is tossed twice, what is the probability of it not landing on its side either time?

2. Each airport across the country has its own 6 digit code #(Manchester314552/Chicago121055). How many different codes can be made, if zero is not allowed as a first digit?

3. Professor Brown gives her students a maximum of 3 attempts to pass a final exam. She has found that the probability of passing on the first attempt is .60, the probability of passing on the second try is .68, and the probability of passing on the third attempt is .85. What is the probability that a randomly selected student of hers will pass the final exam?

4. A sample space is composed of four possible outcomes, called A, B, C, and D. A and B are equally likely, D is four times as probable as A, and C is five times as probable as A. What is the probability of outcome A?

5. Let P(4) be the probability of getting a four when you choose a card from a deck of cards, let

P(F) be the probability of getting a face card from a deck, and P(H) be the probability of getting a heart from the deck.

a. What is P(4 or H)?

b. What is P(4 or F)?

c. What is P(H or F)?

d. Are events 4 and H mutually exclusive?

e. Are events 4 and F mutually exclusive?

f. Are events 4 and H independent?

g. Are events 4 and F independent?

6. 30% of the trees in a particular forest have a disease, 40% are too small to be used for lumber, and 22% are both small and diseased. What % are too small to be used for lumber or have a disease?

7. The ages of students enrolled in the classes at a local community college are given in the following chart.

18-27 28-37 38-47 47+

Male 425 265 125 54

Female 471 149 98 25

Find: a. P(male or 28-37)

b. P(female or 38+)

c. P(18-27 given the person is female)

d. P(28-47)

e. P(47+ and female)

#### Solution Summary

This posting provides solution to various probability problems.