Given P(A) = 0.7 and P(B) = 0.2, do the following. A) If A and B are mutually exclusive events,...

Question:

Given {eq}P(A) = 0.7 {/eq} and {eq}P(B) = 0.2 {/eq}, do the following.

A) If {eq}A {/eq} and {eq}B {/eq} are mutually exclusive events, compute {eq}P(A \, \mathrm{or} \, B) {/eq}.

B) If {eq}P(A \, \mathrm{and} \, B) = 0.1 {/eq}, compute {eq}P(A \, \mathrm{or} \, B) {/eq}.

Events :

Events are the possible outcomes and they form possible outcomes given a certain probability. There are various types of events that are associated with probabilities:

  1. Mutually exclusive events.
  2. Indipendent events.
  3. Mutually inclusive events.

Answer and Explanation:

A) If A and B are mutually exclusive events, compute P(AorB)

If two events are mutually exclusive then the probability of two events occurring is 0.

  • {eq}\text{P(A or B) = P(A) + P(B) - P( A and B)} {/eq}
  • {eq}\text{P(A or B) }= 0.7 + 0.2 - 0 {/eq}
  • {eq}\text{P(A or B) }= 0.9 {/eq}

B) If P(AandB)=0.1 compute P(AorB).

  • {eq}\text{P(A or B) = P(A) + P(B) - P( A and B)} {/eq}
  • {eq}\text{P(A or B) }= 0.7+0.2-0.1 {/eq}
  • {eq}\text{P(A or B) }= 0.8 {/eq}

Learn more about this topic:

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Mutually Exclusive Events & Non-Mutually Exclusive Events

from 6th-8th Grade Math: Practice & Review

Chapter 48 / Lesson 5
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