Math / Data & Statistics

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

Studdy Solution

STEP 1

1. Events A and B are mutually exclusive, meaning they cannot both occur at the same time.
2. The probability of either event A or event B occurring is given by the formula $P(A \text{ or } B) = P(A) + P(B)$ .

STEP 2

1. Use the formula for mutually exclusive events to find $P(A \text{ or } B)$ for each case.

STEP 3

For case (a), apply the formula:
Given $P(A) = 0.35$ and $P(B) = 0.12$ ,
$P(A \text{ or } B) = P(A) + P(B) = 0.35 + 0.12$
$P(A \text{ or } B) = 0.47$

STEP 4

For case (b), apply the formula:
Given $P(A) = \frac{1}{4}$ and $P(B) = \frac{1}{6}$ ,
Convert to a common denominator:
$P(A) = \frac{3}{12}, \quad P(B) = \frac{2}{12}$
$P(A \text{ or } B) = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}$

STEP 5

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

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