daves wardrobe contains 21 t-shirts, of which 17 are gray. dave selects a t-shirt at random.
(a) what is the probability that dave selects a gray t-shirt? enter a fraction in simplest form.
(b) what are the odds in favor of dave selecting a gray t-shirt? make a ratio in simplest form.

question 2
the odds in favor of professor jones being available during his office hours are 13 to 3.
what is the probability that professor jones will be available? give your answer as a fraction in simplest form.

question 3
the weatherman says that there is a 60% chance of rain today.
(a) what is the probability that it will not rain today? give the probability as a percentage.
(b) what are the odds in favor of rain today? give a ratio in simplest form.
(c) what are the odds against rain today? give a ratio in simplest form.

Question

daves wardrobe contains 21 t-shirts, of which 17 are gray. dave selects a t-shirt at random.
(a) what is the probability that dave selects a gray t-shirt? enter a fraction in simplest form.
(b) what are the odds in favor of dave selecting a gray t-shirt? make a ratio in simplest form.

question 2
the odds in favor of professor jones being available during his office hours are 13 to 3.
what is the probability that professor jones will be available? give your answer as a fraction in simplest form.

question 3
the weatherman says that there is a 60% chance of rain today.
(a) what is the probability that it will not rain today? give the probability as a percentage.
(b) what are the odds in favor of rain today? give a ratio in simplest form.
(c) what are the odds against rain today? give a ratio in simplest form.

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Probability and Odds", "Odds in Favor", "Odds Against" ], "current_concepts": [ "Probability and Odds", "Odds in Favor", "Odds Against" ] } ## Solve Question 1 $$ \begin{aligned} &\text{Total T-shirts} = 21,\quad \text{Gray T-shirts} = 17,\quad \text{Not gray T-shirts} = 21 - 17 = 4\ &\text{(a) Probability of gray} = \frac{17}{21}\ &\text{(b) Odds in favor of gray} = \text{Gray} : \text{Not gray} = 17 : 4 \end{aligned} $$ ## Solve Question 2 $$ \begin{aligned} &\text{Odds in favor} = 13 : 3 \implies \text{Favorable outcomes} = 13,\quad \text{Unfavorable outcomes} = 3\ &\text{Total outcomes} = 13 + 3 = 16\ &\text{Probability of being available} = \frac{13}{16} \end{aligned} $$ ## Solve Question 3 $$ \begin{aligned} &\text{Probability of rain } P(R) = 60\% = \frac{60}{100} = \frac{3}{5}\ &\text{(a) Probability of no rain } P(R') = 100\% - 60\% = 40\%\ &\text{(b) Odds in favor of rain} = P(R) : P(R') = 60 : 40 = 3 : 2 \implies 3 \text{ to } 2\ &\text{(c) Odds against rain} = P(R') : P(R) = 40 : 60 = 2 : 3 \implies 2 \text{ to } 3 \end{aligned} $$ ## Question 1 (a) $\frac{17}{21}$ (b) 17 : 4 ## Question 2 $\frac{13}{16}$ ## Question 3 (a) 40 % (b) 3 to 2 (c) 2 to 3 { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Statistics", "Probability and Odds" ] }

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