what is the probability that both events b and c will occur?

$p(b) = \frac{3}{4}$
$p(c) = \frac{3}{5}$

$p(b \text{ and } c) = p(b) \cdot p(c)$
$p(b \text{ and } c) = ?$

Question

what is the probability that both events b and c will occur?

$p(b) = \frac{3}{4}$
$p(c) = \frac{3}{5}$

$p(b \text{ and } c) = p(b) \cdot p(c)$
$p(b \text{ and } c) = ?$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Probability Tree Diagrams" ], "new_concepts": [], "current_concepts": [ "Probability Tree Diagrams", "Compound Probability" ] } ## Identify the given probabilities $$ \begin{aligned} P(B) &= \frac{3}{4} \ P(C) &= \frac{3}{5} \end{aligned} $$ ## Apply the multiplication rule for independent events $$ \begin{aligned} P(B \text{ and } C) &= P(B) \cdot P(C) \ &= \frac{3}{4} \cdot \frac{3}{5} \end{aligned} $$ ## Calculate the final product $$ P(B \text{ and } C) = \frac{9}{20} $$ What is the probability that both events B and C will occur? $P(B) = \frac{3}{4}$ $P(C) = \frac{3}{5}$ $P(B \text{ and } C) = P(B) \cdot P(C)$ $P(B \text{ and } C) =$ $\frac{9}{20}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Probability Tree Diagrams" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given probabilities

Apply the multiplication rule for independent events

Calculate the final product

Answer: