Questions: Use the given information to find the indicated probability. A and B are mutually exclusive. P(A)=0.7, P(B)=0.1. Find P((A ∪ B)′). P((A ∪ B)′)=

Transcript text: Use the given information to find the indicated probability. $A$ and $B$ are mutually exclusive. $P(A)=0.7, $P(B)=0.1$. Find $P\left((A \cup B)^{\prime}\right)$. $P\left((A \cup B)^{\prime}\right)=$ $\square$

Solution

Solution Steps

To find the probability of the complement of the union of two mutually exclusive events $A$ and $B$, we can use the following steps:

Calculate the probability of the union of $A$ and $B$.
Use the complement rule to find the probability of the complement of the union.

Step 1: Calculate $ P(A \cup B) $

Since $ A $ and $ B $ are mutually exclusive, we can find the probability of their union using the formula: \[ P(A \cup B) = P(A) + P(B) = 0.7 + 0.1 = 0.8 \]

Step 2: Calculate $ P((A \cup B)') $

To find the probability of the complement of the union, we use the complement rule: \[ P((A \cup B)') = 1 - P(A \cup B) = 1 - 0.8 = 0.2 \]