Questions: Suppose L and M are not mutually exclusive events with P(L)=0.45, P(M)=0.55, P(L and M)=0.2. Find P(L or M).

Transcript text: Suppose $L$ and $M$ are not mutually exclusive events with $P(L)=0.45, P(M)=0.55, P(L$ and $M)=0.2 \quad$ Find $P(L$ or $M)$.

Solution

Solution Steps

To find the probability of either event $ L $ or event $ M $ occurring, we use the formula for the probability of the union of two events:

\[ P(L \text{ or } M) = P(L) + P(M) - P(L \text{ and } M) \]

This formula accounts for the overlap between the two events, which is subtracted to avoid double-counting.

Step 1: Given Probabilities

We are given the following probabilities:

$ P(L) = 0.45 $
$ P(M) = 0.55 $
$ P(L \text{ and } M) = 0.2 $

Step 2: Apply the Union Formula

To find $ P(L \text{ or } M) $, we use the formula for the probability of the union of two events: \[ P(L \text{ or } M) = P(L) + P(M) - P(L \text{ and } M) \]

Step 3: Substitute Values

Substituting the given values into the formula: \[ P(L \text{ or } M) = 0.45 + 0.55 - 0.2 \]

Step 4: Perform the Calculation

Calculating the expression: \[ P(L \text{ or } M) = 1.0 - 0.2 = 0.8 \]

Final Answer

Thus, the probability of either event $ L $ or event $ M $ occurring is \[ \boxed{P(L \text{ or } M) = 0.8} \]

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