Math  /  Data & Statistics

Question7. Event A and Event B are mutually exclusive events. Find P(AP(A or B)B) for each of the following: (a) P(A)=0.35,P(B)=0.12P(A)=0.35, P(B)=0.12 (b) P(A)=14,P(B)=16P(A)=\frac{1}{4}, P(B)=\frac{1}{6} (c) P(A)=322,P(B)=7110P(A)=\frac{3}{22}, P(B)=\frac{7}{110}

Studdy Solution
For case (c), apply the formula:
Given P(A)=322 P(A) = \frac{3}{22} and P(B)=7110 P(B) = \frac{7}{110} ,
Convert to a common denominator:
P(A)=15110,P(B)=7110 P(A) = \frac{15}{110}, \quad P(B) = \frac{7}{110}
P(A or B)=15110+7110=22110 P(A \text{ or } B) = \frac{15}{110} + \frac{7}{110} = \frac{22}{110}
Simplify:
P(A or B)=15 P(A \text{ or } B) = \frac{1}{5}
The probabilities are: (a) 0.47 \boxed{0.47} (b) 512 \boxed{\frac{5}{12}} (c) 15 \boxed{\frac{1}{5}}

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