In an experiment, the probability that event A occurs is 3/7, the probability that event B occurs is 1/2, and the probability that events A and B both occur is 3/8. What is the probability that A occurs given that B occurs? Simplify any fractions. ____

Use Conditional Probability Formula: To find the probability that A occurs given that B occurs, we use the formula for conditional probability: P(A|B) = P(A and B) / P(B).Calculate P(A|B): We know P(A and B) = 3/8 and P(B) = 1/2.Multiply Fractions: Now, let's do the calculation: P(A|B) = (3/8) / (1/2).Simplify Multiplication: To divide by a fraction, we multiply by its reciprocal. So, P(A|B) = (3/8) * (2/1).Reduce Fraction: Multiplying the fractions, we get P(A|B) = (3*2) / (8*1).Final Probability: Simplifying the multiplication, P(A|B) = 6/8.We can reduce the fraction 6/8 by dividing both numerator and denominator by 2.After simplifying, we get P(A|B) = 3/4.

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In an experiment, the probability that event $A$ occurs is $\frac{3}{7}$ , the probability that event $B$ occurs is $\frac{1}{2}$ , and the probability that events $A$ and $B$ both occur is $\frac{3}{8}$ . What is the probability that $A$ occurs given that $B$ occurs? Simplify any fractions.

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Precalculus

Find conditional probabilities

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Q. In an experiment, the probability that event

A

occurs is

\frac{3}{7}

, the probability that event

B

occurs is

\frac{1}{2}

, and the probability that events

A

and

B

both occur is

\frac{3}{8}

. What is the probability that

A

occurs given that

B

occurs? Simplify any fractions.

Use Conditional Probability Formula: To find the probability that $A$ occurs given that $B$ occurs, we use the formula for conditional probability: $P(A|B) = \frac{P(A \text{ and } B)}{P(B)}$ .
Calculate $P(A|B)$ : We know $P(A \text{ and } B) = \frac{3}{8}$ and $P(B) = \frac{1}{2}$ .
Multiply Fractions: Now, let's do the calculation: $P(A|B) = \frac{3}{8} / \frac{1}{2}.$
Simplify Multiplication: To divide by a fraction, we multiply by its reciprocal. So, $P(A|B) = \frac{3}{8} \times \frac{2}{1}.$
Reduce Fraction: Multiplying the fractions, we get $P(A|B) = \frac{3 \times 2}{8 \times 1}$ .
Final Probability: Simplifying the multiplication, $P(A|B) = \frac{6}{8}$ .
Final Probability: Simplifying the multiplication, $P(A|B) = \frac{6}{8}$ .We can reduce the fraction $\frac{6}{8}$ by dividing both numerator and denominator by $2$ .
Final Probability: Simplifying the multiplication, $P(A|B) = \frac{6}{8}$ .We can reduce the fraction $\frac{6}{8}$ by dividing both numerator and denominator by $2$ .After simplifying, we get $P(A|B) = \frac{3}{4}$ .