Question

1. the blue jays have been given odds in favour of winning their next game at 4:9. if i bet $20 they will win, how much profit could i make?

a. $65
b. $8.89
c. $52.50
d. $45
e. none of these

1. kyaan can hit a target 25% of the time. what is the probability that he will hit his target at least once in 4 shots?

a. 10.55%
b. 0.39%
c. 31.64%
d. 68.36%
e. none of these

Explanation:

Question 7

Step 1: Understand Odds and Profit Calculation

Odds in favor of winning are \(4:9\). This means for every \(9\) units bet, we win \(4\) units (profit) if we win. We bet \(\$20\). Let's set up a proportion. Let \(x\) be the profit. The ratio of profit to bet amount should be equal to the ratio of the favorable odds part to the unfavorable odds part. So, \(\frac{x}{20}=\frac{4}{9}\).

Step 2: Solve for \(x\)

To find \(x\), we cross - multiply: \(x=\frac{4\times20}{9}=\frac{80}{9}\approx8.89\).

Step 1: Probability of Not Hitting

The probability of Ky aan not hitting the target in a single shot is \(1 - 0.25=0.75\) (since the probability of hitting is \(25\% = 0.25\)).

Step 2: Probability of Not Hitting in 4 Shots

The probability of not hitting the target in 4 independent shots is \((0.75)^4\) (because for independent events, the probability of all events occurring is the product of their individual probabilities). \((0.75)^4 = 0.75\times0.75\times0.75\times0.75=\frac{3}{4}\times\frac{3}{4}\times\frac{3}{4}\times\frac{3}{4}=\frac{81}{256}\approx0.3164\).

Step 3: Probability of Hitting at Least Once

The probability of hitting the target at least once in 4 shots is the complement of not hitting at all. So, \(P(\text{at least once})=1 - P(\text{not at all}) = 1-(0.75)^4\).
\(1 - 0.3164 = 0.6836\) or \(68.36\%\approx68.36\%\), which is option d.

Answer:

b. \$8.89

Question 8