use the definitions given in the text to find both the odds for and the odds against the following event.

flipping 2 fair coins and getting exactly 1 head.

the odds for getting exactly 1 head are 1 to 1.
(type a whole number.)

the odds against getting exactly 1 head are to
(type a whole number.)

Question

use the definitions given in the text to find both the odds for and the odds against the following event.

flipping 2 fair coins and getting exactly 1 head.

the odds for getting exactly 1 head are 1 to 1.
(type a whole number.)

the odds against getting exactly 1 head are   to
(type a whole number.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Odds For and Against", "Fair Coin Probability" ], "new_concepts": [], "current_concepts": [ "Odds For and Against", "Fair Coin Probability" ] } ## Determine sample space and event outcomes $$ \begin{aligned} S &= \{HH, HT, TH, TT\} \ n(S) &= 4 \ E &= \{HT, TH\} \ n(E) &= 2 \ n(E') &= n(S) - n(E) = 4 - 2 = 2 \end{aligned} $$ ## Calculate odds for the event $$ \begin{aligned} \text{Odds for } E &= n(E) : n(E') \ &= 2 : 2 \ &= 1 : 1 \end{aligned} $$ ## Calculate odds against the event $$ \begin{aligned} \text{Odds against } E &= n(E') : n(E) \ &= 2 : 2 \ &= 1 : 1 \end{aligned} $$ The odds for getting exactly 1 head are 1 to 1. (Type a whole number.) The odds against getting exactly 1 head are 1 to 1. (Type a whole number.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Odds For and Against" ] }

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QUESTION IMAGE

Question

Explanation:

Determine sample space and event outcomes

Calculate odds for the event

Calculate odds against the event

Answer: