Questions: Question If A and B are independent events with P(A)=0.60 and P(A AND B)=0.30, find P(B). Provide your answer below:

Transcript text: Question If $A$ and $B$ are independent events with $P(A)=0.60$ and $P(A$ AND $B)=0.30$, find $P(B)$. Provide your answer below: $\square$ FEEDBACK MORE INSTRUCTION SUBMIT

Solution

Solution Steps

Step 1: Understand the Problem

Given that $A$ and $B$ are independent events, we need to find the probability of event $B$, denoted as $P(B)$. We are given the probability of event $A$ occurring, $P(A)$, and the probability of both $A$ and $B$ occurring together, $P(A$ AND $B)$.

Step 2: Apply the Formula for Independent Events

For independent events, the probability of both events occurring together is the product of their individual probabilities. Thus, $P(A$ AND $B) = P(A) \times P(B)$. Given $P(A)$ and $P(A$ AND $B)$, we can rearrange the formula to solve for $P(B)$: \[P(B) = \frac{P(A \text{ AND } B)}{P(A)}\]

Step 3: Substitute the Given Values and Calculate

Substituting the given values, $P(A) = 0.6$ and $P(A$ AND $B) = 0.3$, into the formula, we get: \[P(B) = \frac{0.3}{0.6}\] After calculation, $P(B) = 0.5$, rounded to 2 decimal places.