Question

1. high blood pressure according to the u.s. centers for disease control and prevention, 31% of adults in the united states have high blood pressure. if an adult was randomly selected, determine the odds

a) against the adult having high blood pressure.
b) in favor of the adult having high blood pressure.

1. horseracing the odds against fedora winning the triple crown in horse racing are 82 : 3. determine the probability that fedora wins the triple crown.
2. fair price at a game of chance, the expected value is determined to be -$2.50, and the cost to play the game is $6.50. determine the fair price to play the game.
3. fair price the expected value when you purchase a lottery ticket is -$1.50, and the cost of the lottery ticket is $5.00. determine the fair price of the lottery ticket.

Explanation:

14.

Step1: Recall odds - against formula

Odds against an event $E$ is $\frac{P(\text{not }E)}{P(E)}$. Given $P(\text{high blood pressure}) = 0.31$, then $P(\text{not high blood pressure})=1 - 0.31 = 0.69$.

Step2: Calculate odds - against

The odds against the adult having high blood pressure is $\frac{0.69}{0.31}=\frac{69}{31}$.

Step3: Recall odds - in - favor formula

Odds in favor of an event $E$ is $\frac{P(E)}{P(\text{not }E)}$.

Step4: Calculate odds - in - favor

The odds in favor of the adult having high blood pressure is $\frac{0.31}{0.69}=\frac{31}{69}$.

Step1: Recall odds to probability formula

If the odds against an event $E$ is $a:b$, then the probability of the event $E$ is $P(E)=\frac{b}{a + b}$. Here, $a = 82$ and $b = 3$.

Step2: Calculate probability

$P(\text{Fedora wins})=\frac{3}{82+3}=\frac{3}{85}$.

Step1: Recall fair - price formula

The fair price $F$ of a game is given by $F=\text{Cost}-\text{Expected value}$. Given $\text{Expected value}=- 2.50$ and $\text{Cost}=6.50$.

Step2: Calculate fair price

$F = 6.50-(-2.50)=6.50 + 2.50=9$.

Answer:

a) $\frac{69}{31}$
b) $\frac{31}{69}$

16.