two coins are tossed.
event a: the first coin does not land on tails.
event b: the second coin does land on heads.
what is the probability that both events will occur?
$p(a \text{ and } b) = \quad\%$
for independent events: $p(a \text{ and } b) = p(a) \cdot p(b)$
round your answer to the nearest whole percent.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Theoretical Probability", "Sample Space" ], "new_concepts": [ "Independent Events", "Probability of Intersection" ], "current_concepts": [ "Theoretical Probability", "Sample Space", "Independent Events", "Probability of Intersection" ] } ## Identify the sample space of tossing two coins $$ S = \{HH, HT, TH, TT\} $$ ## Determine the outcomes for Event A and Event B $$ \begin{aligned} A &= \{HH, HT\} \implies P(A) = \frac{2}{4} = 0.5 \ B &= \{HH, TH\} \implies P(B) = \frac{2}{4} = 0.5 \end{aligned} $$ ## Calculate the probability of both events occurring $$ \begin{aligned} P(A \text{ and } B) &= P(A) \cdot P(B) \ &= 0.5 \cdot 0.5 \ &= 0.25 \ &= 25\% \end{aligned} $$ Two coins are tossed. Event A: The first coin does NOT land on tails. Event B: The second coin does land on heads. What is the probability that both events will occur? $P(A \text{ and } B) =$ 25% { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Probability of Independent Events" ] }

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Question

Explanation:

Identify the sample space of tossing two coins

Determine the outcomes for Event A and Event B

Calculate the probability of both events occurring

Answer: