Math Problem Statement

Let and be mutually exclusive events, such that and . Find the following probabilities:

P(A and B)= % (Round the answer to 2 decimals)

P(A or B)= % (Round the answer to 2 decimals)

Solution

To solve these probabilities, let's use the following standard probability rules:

  • For mutually exclusive events, P(A and B)=0P(A \text{ and } B) = 0. This is because mutually exclusive events cannot happen at the same time.

  • For the probability of P(A or B)P(A \text{ or } B), use the formula: P(A or B)=P(A)+P(B)P(A and B)P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) Since P(A and B)=0P(A \text{ and } B) = 0, the formula simplifies to: P(A or B)=P(A)+P(B)P(A \text{ or } B) = P(A) + P(B)

Now let's solve:

  1. P(A and B)=0P(A \text{ and } B) = 0
  2. P(A or B)=P(A)+P(B)P(A \text{ or } B) = P(A) + P(B)

To finalize the calculations, I need the values of P(A)P(A) and P(B)P(B). Could you provide those probabilities?

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Math Problem Analysis

Mathematical Concepts

Probability
Mutually Exclusive Events

Formulas

P(A and B) = 0 (for mutually exclusive events)
P(A or B) = P(A) + P(B)

Theorems

Mutually Exclusive Events Theorem

Suitable Grade Level

Grades 9-11