a probability experiment consists of rolling a six-sided die and spinning the spinner shown at the right. the spinner is equally likely to land on each color. use a tree diagram to find the probability of the given event. then tell whether the event can be considered unusual.

event: rolling a number less than 2 and the spinner landing on blue

the probability of the event is
(type an integer or decimal rounded to three decimal places as needed.)

Question

a probability experiment consists of rolling a six-sided die and spinning the spinner shown at the right. the spinner is equally likely to land on each color. use a tree diagram to find the probability of the given event. then tell whether the event can be considered unusual.

event: rolling a number less than 2 and the spinner landing on blue

the probability of the event is
(type an integer or decimal rounded to three decimal places as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Independent Events Probability", "Sample Space Outcomes" ], "new_concepts": [], "current_concepts": [ "Independent Events Probability", "Sample Space Outcomes", "Classical Probability" ] } ## Determine the probability of rolling a number less than 2 Using the *Sample Space Outcomes* and *Classical Probability* knowledge points $$ \begin{aligned} &S_{\text{die}} = \{1, 2, 3, 4, 5, 6\} \ &\text{Event } A = \{x \in S_{\text{die}} \mid x < 2\} = \{1\} \ &P(A) = \frac{1}{6} \approx 0.167 \end{aligned} $$ ## Determine the probability of the spinner landing on blue Using the *Sample Space Outcomes* and *Classical Probability* knowledge points $$ \begin{aligned} &S_{\text{spinner}} = \{\text{Red}, \text{Blue}, \text{Green}, \text{Yellow}\} \ &\text{Event } B = \{\text{Blue}\} \ &P(B) = \frac{1}{4} = 0.25 \end{aligned} $$ ## Calculate the joint probability of both independent events Using the *Independent Events Probability* knowledge point $$ \begin{aligned} &P(A \text{ and } B) = P(A) \times P(B) \ &P(A \text{ and } B) = \frac{1}{6} \times \frac{1}{4} = \frac{1}{24} \ &P(A \text{ and } B) \approx 0.042 \end{aligned} $$ The probability of the event is $0.042$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Independent Events Probability" ] }

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Question

Explanation:

Determine the probability of rolling a number less than 2

Determine the probability of the spinner landing on blue

Calculate the joint probability of both independent events

Answer: