Questions: Find the probability P(E or F) if E and F are mutually exclusive, P(E)=0.25, and P(F)=0.51.

Transcript text: Find the probability $P(E$ or $F)$ if $E$ and $F$ are mutually exclusive, $P(E)=0.25$, and $P(F)=0.51$.

Solution

Solution Steps

To find the probability $ P(E \text{ or } F) $ when events $ E $ and $ F $ are mutually exclusive, we can use the formula for the probability of the union of two mutually exclusive events: $ P(E \text{ or } F) = P(E) + P(F) $. Since the events are mutually exclusive, there is no overlap between them, and thus no need to subtract any intersection probability.

Step 1: Given Probabilities

We are given the probabilities of events $ E $ and $ F $: \[ P(E) = 0.25, \quad P(F) = 0.51 \]

Step 2: Apply the Formula for Mutually Exclusive Events

Since $ E $ and $ F $ are mutually exclusive, we can use the formula for the probability of the union of two mutually exclusive events: \[ P(E \text{ or } F) = P(E) + P(F) \]

Step 3: Calculate the Probability

Substituting the given values into the formula: \[ P(E \text{ or } F) = 0.25 + 0.51 = 0.76 \]