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Chapter 5: Q 2.3. (page 305)

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

Short Answer

Expert verified

The likelihood of P(AorB)鈮�P(A)+P(B)and the occurrence A or B

Step by step solution

01

Step 1. Given Information    

P(AorB)鈮�P(A鈭�B)P(AorB)鈮�P(A)+P(B)

02

Step 2. Concept Used   

Definition of the probability addition theorem: Assume Aand Bare two events in a random experiment, and you want to know whether Aor Bhas a higher likelihood. Then apply the probability addition theorem.

03

Step 3. Calculation    

let A and B be two events of a random experiment using the addition theorem of probability. That isP(AorB)=P(A鈭�B)P(AorB)=P(A)+P(B)鈭�P(A鈭�B)

If A and B are not mutually exclusive events. So, P(A鈭�B)鈮�0P(AorB)鈮�P(A)+P(B)

Therefore, The event and the probability of P(AorB)鈮�P(A)+P(B)

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Most popular questions from this chapter

Inspecting switches A shipment contains 10,000switches. Of these, 1000 are bad. An inspector draws 2 switches at random, one after the other.

(a) Draw a tree diagram that shows the sample space of this chance process.

(b) Find the probability that both switches are defective.

Find P(AandB).

Use the correct choice from the previous question and these random digits to simulate 10 shots:8273471490204674751181676553009438314893How many of these 10 shots are hits? (a) 2(b) 3(c) 4(d) 5(e) 6

Roulette, An American roulette wheel has38slots with numbers 1through 36,0,and00,as shown in the figure. Of the numbered slots, 18are red, 18are black, and 2鈥攖丑别 0and 00鈥攁re green. When the wheel is spun, a metal ball is dropped onto the middle of the wheel. If the wheel is balanced, the ball

is equally likely to settle in any of the numbered slots. Imagine spinning a fair wheel once. Define events B: ball lands in a black slot, and E: ball lands in an even numbered slot. (Treat 0and 00as even numbers.)

(a) Make a two-way table that displays the sample space in terms of events B and E.

(b) Find P(B) and P(E).

(c) Describe the event 鈥淏 and E鈥� in words. Then find P(B and E). Show your work.

(d) Explain why P(B or E) 鈮� P(B) + P(E). Then use the general addition rule to compute P(B or E).

IfC is the event that the person chosen has normal cholesterol (below 200 mg/dl), what鈥檚 P(C)?
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