Question

suppose the spinner shown to the right is spun once, to determine a single - digit number, a that the resulting number is odd. assume all sectors of the spinner are the same size.
determine each of the following.
(a) the sample space
(b) the number of favorable outcomes
(c) the number of unfavorable outcomes
(d) the total number of possible outcomes
(e) the probability of an odd number
(f) the odds in favor of an odd number
(c) identify the number of unfavorable outcomes.
there is/are 2 unfavorable outcome(s).
(type a whole number.)
(d) identify the total number of possible outcomes.
there are 3 possible outcomes.
(type a whole number.)
(e) identify the probability of an odd number.
the probability of an odd number is \\( \frac { 1 } { 3 } \\).
(type an integer or a simplified fraction.)
(f) identify the odds in favor of an odd number.
the odds in favor of an odd number are \\( \square \\) to \\( \square \\).
(type whole numbers.)

Explanation:

Step1: Recall the formula for odds in favor

The formula for odds in favor of an event \(E\) is \(\text{Odds in favor}=\frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}}\)

Step2: Identify the number of favorable and unfavorable outcomes

From part (b) (assuming the number of favorable outcomes is \(1\) as per the probability \(\frac{1}{3}\), since \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\), and total number of outcomes \(n = 3\)), number of favorable outcomes \(= 1\). From part (c), number of unfavorable outcomes \(= 2\)

Step3: Calculate the odds in favor

Using the formula \(\text{Odds in favor}=\frac{1}{2}\), which means the odds are \(1\) to \(2\)

Answer:

The odds in favor of an odd number are \(1\) to \(2\)