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Chapter 5: Q 2.2. (page 305)

Find P(AandB).

Short Answer

Expert verified

P(AandB)=P(A).P(B)

Step by step solution

01

Step 1. Given Information   

A and B are separate events, whereas P(AandB)is a combination of the two.

02

Step 2. Concept Used   

Separate events: Assume A and B are two independent events in sample space that are associated with a random experiment.

03

Step 3. Explanation  

Independent events are defined as two independent events of sample space related with a random experiment P(AandB)=P(A).P(B).If the problem is made up of words, it signifies the elements have been multiplied. As a result, Aand Bare separate events.

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Most popular questions from this chapter

Myspace versus Facebook A recent survey suggests that 85% of college students have posted a profile on Facebook, 54%use Myspace regularly, and 42% do both. Suppose we select a college student at random.

(a) Assuming that there are 20 million college students, make a two-way table for this chance process.

(b) Construct a Venn diagram to represent this setting.

(c) Consider the event that the randomly selected college student has posted a profile on at least one of these two sites. Write this event in symbolic form

using the two events of interest that you chose in (b).

(d) Find the probability of the event described in (c).

Explain your method.

Explain why P(AorB)≠P(A)+P(B). Then use the general addition rule to findP(AorB).

At the gym Suppose that 10%of adults belong to health clubs, and 40% of these health club members go to the club at least twice a week. What percent of all adults go to a health club at least twice a week? Write the information given in terms of probabilities, and use the general multiplication rule.

Who eats breakfast? Refer to Exercise 49.

(a) Construct a Venn diagram that models the chance process using events B: eats breakfast regularly, and M: is male.

(b) Find P(B∪M) Interpret this value in context.

(c) Find P(Bc∩Mc) Interpret this value in context.

Simulation blunders Explain what’s wrong with each of the following simulation designs.

(a) A roulette wheel has 38colored slots—38 red, 18 black, and 2green. To simulate one spin of the wheel, let numbers 00 to 18 represent red, 19 to 37

represent black, and 38 to 40 represent green.

(b) About 10% of U.S. adults are left-handed. To simulate randomly selecting one adult at a time until you find a left-hander, use two digits. Let 01 to 10 represent being left-handed and 11 to 00 represent being right-handed. Move across a row in Table D, two digits at a time, skipping any numbers that have already appeared, until you find a number between 01 and 10. Record the number of people selected.
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