Two events A and B are mutually exclusive. If P(A) = 0.27 and P(A or B) =0.61 and P(A and B) =...

Question:

Two events A and B are mutually exclusive.

If P(A) = 0.27 and P(A or B) =0.61 and P(A and B) = 0.14, then P(B) = ?

Probability:

The probability is one of the most important concepts of the statistics. The probability is a happening of an event. The limit of the probability is from zero to one inclusively. The probability of an impossible event is zero.

Answer and Explanation:

Given that,

{eq}P(A) = 0.27\\ P(A \ or \ B) = 0.61\\ P(A \ and \ B) = 0.14\\ {/eq}


The additional proability rule is defined as:

{eq}P(A \ and \ B) = P(A) + P(B) -P(A \ or \ B)\\ 0.14= 0.27 + P(B) - 0.61\\ P(B) = 0.14 + 0.34\\ \color{blue}{P(B) = 0.48} {/eq}


Learn more about this topic:

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The Addition Rule of Probability: Definition & Examples

from Statistics 101: Principles of Statistics

Chapter 4 / Lesson 10
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