Question 38 of 55beginner🔧 ApplyShort Answer2 marks

Given P(A) = 3/5 and P(B) = 1/5. Find P(A or B), if A and B are mutually exclusive events.

Correct Answer

Since A and B are mutually exclusive events, the occurrence of one event prevents the occurrence of the other. According to the rules provided in the context, for mutually exclusive events, the probability of 'A or B' is simply the sum of their individual probabilities.

Using the formula: P(A or B) = P(A) + P(B)

We substitute the given values: P(A or B) = 3/5 + 1/5

Performing the addition: P(A or B) = (3 + 1)/5 = 4/5

Therefore, the probability that event A or event B occurs is 4/5.

Exercise: EXERCISE 14.2 | Q: 14 | (Page Page 17)
For More Understanding

Explanation

The question requires calculating P(A or B) for mutually exclusive events. The provided context explicitly states the rule: 'If A and B are mutually exclusive, then P(A or B) = P(A) + P(B)'. By substituting the given values P(A) = 3/5 and P(B) = 1/5 into this addition rule, we find the sum to be 4/5. The context also lists the general formula P(A or B) = P(A) + P(B) - P(A and B), but for mutually exclusive events, the intersection term is effectively zero, reducing the formula to the one used.

Solution Steps

  1. Step 1: Identify the formula for mutually exclusive events from the context: P(A or B) = P(A) + P(B).

  2. Step 2: Substitute the given probabilities into the formula: P(A or B) = 3/5 + 1/5.

  3. Step 3: Add the fractions: P(A or B) = 4/5.

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