MIRAMAR COLLEGE/FALL 2020 MATH 119
MATH 119 WORKSHEET 3
Prof. To
ez
NAME: REEM
Instructions: WORKSHEET #3 is worth 5 points. Show calculations for full credit. You may use you pencil, calculators, and/or Statcrunch. No late work will be accepted.
There are 23 countries in North America, 12 countries in South America, 47 countries in Europe, 44 countries in Asia, 54 countries in Africa, and 14 in Oceania (Pacific Ocean region). Let A = the event that a country is in Asia. Let E = the event that a country is in Europe. Let F = the event that a country is in Africa. Let N = the event that a country is in North America. Let O = the event that a country is in Oceania. Let S = the event that a country is in South America.
Exercise 1.
Solution
1a. Find P(A).
1a.
1b. Find P(E).
1b.
1c. Find P(O).
1c.
1d. Find P(F).
1d.
1e. Find P(S).
1e.
Exercise 2. Consider a standard deck of cards of 52 cards.
Solution
2a. What is the probability of drawing a red card?
2a.
2b. What is the probability of drawing a club?
2b.
Consider a fair, six-sided die numbered one through six.
2c. What is the probability of rolling an even number of dots?
2c.
2d. What is the probability of rolling a prime number of dots?
2d.
Exercise 3. A special deck of cards has ten cards. Four are green, three are blue, and three are red. When a
card is picked, its color is recorded. An experiment consists of first picking a card and then tossing a coin. Explain your answer in one to three complete sentences, including numerical justification.
Solution
3a. List the sample space.
3a.
3b. Let A be the event that a blue card is picked first, followed by landing a head on the coin toss. Find P(A).
3b.
3c. Let B be the event that a red or green is picked, followed by landing a head on the coin toss. Are the events A and B mutually exclusive?
3c.
3d. Let C be the event that a red or blue card is picked, followed by landing a head on the coin toss. Are the events A and C mutually exclusive?
3d.
Exercise 4.
Solution
Consider the following scenario:
Let P(C) = 0.4.
Let P(D) = 0.5.
Let P(C|D) = 0.6.
4a. Find P (C AND D).
4a.
4b. Are C and D mutually exclusive? Why or why not?
4b.
4c. Are C and D independent events? Why or why not?
4c.
4d. Find P (C OR D).
4d.
4e. Find P(D|C).
4e.
Exercise 5. A deck of 10 cards consists of 6 green and 4 yellow cards.
Solution
Suppose that you randomly draw two cards, one at a time, without replacement.
G1 = first card is green
G2 = second card is green
5a. Draw a tree diagram of the situation.
5a.
5b. Find P (G1 AND G2).
5b.
5c. Find P (at least one green).
5c.
5d. Find P (G2|G1).
5d.
5e. Are G2 and G1 independent events? Explain why or why not.
5e.
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