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Chapter 3: Q. 3.27 (page 204)

Suppose an experiment has outcomes black, white, red, orange, yellow, green, blue, and purple, where each outcome has an equal chance of occurring. Let event C = {green, blue, purple} and event P = {red, yellow, blue}. Then

C AND P = {blue} and C OR P = {green, blue, purple, red, yellow}. Draw a Venn diagram representing this situation.

Short Answer

Expert verified

The Venn diagram is as follows:

Step by step solution

01

Given Information

Suppose an experiment has outcomes black, white, red, orange, yellow, green, blue and purple, where each outcome has as equal chance of occurring. Let event C={ green, blue, purple } and event P={ red, yellow, blue }. Then C AND P={ blue } and C OR P={ green, blue, purple, red, yellow } .

02

Calculation

We have

Event C={ green, blue, purple }

Event P={ red, yellow, blue }.

C AND P ={ blue }

C OR P={ green, blue, purple, red, yellow }

Thus, Venn diagram is as follows

03

Conclusion

Hence, the Venn diagram representing the solution is sketched.

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Most popular questions from this chapter

An experiment consists of tossing a nickel, a dime, and a quarter. Of interest is the side the coin lands on.

a. List the sample space.

b. Let A be the event that there are at least two tails. Find PA.

c. Let Bbe the event that the first and second tosses land on heads. Are the events A and B mutually exclusive?

Explain your answer in one to three complete sentences, including justification.

E and F are mutually exclusive events. P(E) = 0.4; P(F) = 0.5. Find P(E鈭).

What is the sum of the probabilities of an event and its complement?

A box is filled with several party favors. It contains 12

hats, 15 noisemakers, ten finger traps, and five bags of confetti.

Let H = the event of getting a hat.

Let N = the event of getting a noisemaker.

Let F = the event of getting a finger trap.

Let C = the event of getting a bag of confetti.

Find P(N).

When the Euro coin was introduced in 2002, two math professors had their statistics students test whether the Belgian one Euro coin was a fair coin. They spun the coin rather than tossing it and found that out of 250spins,140showed a head (event H) while 110showed a tail (event T). On that basis, they claimed that it is not a fair coin.

a. Based on the given data, find P(H) and P(T).

b. Use a tree to find the probabilities of each possible outcome for the experiment of tossing the coin twice.

c. Use the tree to find the probability of obtaining exactly one head in two tosses of the coin.

d. Use the tree to find the probability of obtaining at least one head
See all solutions

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