Chapter 3: Q. 91 (page 224)

Yand Zare independent events.
a. Rewrite the basic Addition Rule $P (Y O R Z) = P (Y) + P (Z) - P (Y A N D Z)$ using the information that Y and Z are independent events.
b. Use the rewritten rule to findP(Z) if $P (Y O R Z) = 0.71$ and $P (Y) = 0.42$

Short Answer

Expert verified

(a) $P (Y O R Z) = P (Y) + P (Z) - P (Y) P (Z)$ .

(b) $P (Z) = 0.5$ .

Step by step solution

Given information (part a)

Y andZ are independent events.

Explanation (part a)

The addition rule states that

$P (Y o r Z) = P (Y) + P (Z) - P (Y a n d Z)$

Also, given that Yand Z are independent events

Thus, we have $P (Y a n d Z) = P (Y) P (Z)$

Substituting the value in the above rule, we get

$P (Y o r Z) = P (Y) + P (Z) - P (Y) P (Z)$

Given information (part b)

Y and Z are independent events. $P (Y o r Z) = 0.71 and P (Y) = 0.42$

Explanation (part b)

The addition rule states that

$P (Y O R Z) = P (Y) + P (Z) - P (Y A N D Z)$

Also, given that Y andZ are independent events

Thus, we have $P (Y a n d Z) = P (Y) P (Z)$

Substituting the value in the above rule, we get

$P (Y \cap Z) = P (Y) + P (Z) - P (Y) P (Z) P (Y \cap Z) = P (Y) + P (Z) - P (Y) P (Z)$

Now, we have

$P (Y o r Z) = 0.71 P (Y) = 0.42$

Substituting the values, we get

$0.71 = 0.42 + P (Z) - (0.42 \times P (Z)) 0.71 = 0.42 + [P (Z) (1 - 0.42)] 0.71 = 0.42 + 0.58 P (Z) P (Z) = \frac{0.71 - 0.42}{0.58} P (Z) = 0.5$

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Yand Zare independent events.
a. Rewrite the basic Addition Rule $P (Y O R Z) = P (Y) + P (Z) - P (Y A N D Z)$ using the information that Y and Z are independent events.
b. Use the rewritten rule to findP(Z) if $P (Y O R Z) = 0.71$ and $P (Y) = 0.42$

Short Answer

Step by step solution

Given information (part a)

Explanation (part a)

Given information (part b)

Explanation (part b)

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Yand Zare independent events.a. Rewrite the basic Addition Rule P(YORZ)=P(Y)+P(Z)-P(YANDZ)using the information that Y and Z are independent events.b. Use the rewritten rule to findP(Z) if P(YORZ)=0.71and PY=0.42

Short Answer

Step by step solution

Given information (part a)

Explanation (part a)

Given information (part b)

Explanation (part b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Discrete Mathematics

Decision Maths

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Yand Zare independent events.
a. Rewrite the basic Addition Rule $P (Y O R Z) = P (Y) + P (Z) - P (Y A N D Z)$ using the information that Y and Z are independent events.
b. Use the rewritten rule to findP(Z) if $P (Y O R Z) = 0.71$ and $P (Y) = 0.42$