Question

1. a grammy award winner must choose from one of 4 dresses, 3 earrings, and 2 heels. how many choices are there? a. 6 b. 8 c. 12 d. 24 e. none of the above 10. find the probability of getting exactly two tails if 3 coins are flipped. a. \\( \frac { 1 } { 8 } \\) b. \\( \frac { 2 } { 8 } \\) c. \\( \frac { 3 } { 8 } \\) d. \\( \frac { 4 } { 8 } \\) e. none of the above 11. you roll a single six - sided die. find the odds in favor of rolling a 3. a. \\( \frac { 1 } { 6 } \\) b. \\( \frac { 1 } { 5 } \\) c. \\( \frac { 4 } { 6 } \\) d. \\( \frac { 3 } { 5 } \\) e. none of the above

Explanation:

Question 9

Step1: Use the counting principle

The counting principle states that if there are \(m\) ways to do one thing, \(n\) ways to do a second thing, and \(p\) ways to do a third thing, then the total number of ways to do all three things is \(m\times n\times p\).
Here, \(m = 4\) (number of dresses), \(n=3\) (number of earrings), and \(p = 2\) (number of heels).

Step2: Calculate the number of choices

The number of choices is \(4\times3\times2=\$24\).

Question 10

Step1: List all possible outcomes

When flipping 3 coins, the sample space \(S\) has \(2\times2\times2 = 8\) possible outcomes. The sample space \(S=\{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}\)

Step2: Count the number of favorable outcomes

The number of outcomes with exactly 2 tails: \(\{HTT, THT, TTH\}\), so \(n = 3\)

Step3: Calculate the probability

The probability \(P=\frac{n}{N}\), where \(n\) is the number of favorable outcomes and \(N\) is the number of total outcomes. So \(P=\frac{3}{8}\)

Question 11

Step1: Determine the number of favorable and unfavorable outcomes

When rolling a six - sided die, the number of favorable outcomes (rolling a 3) is \(n(F)=1\). The number of unfavorable outcomes (not rolling a 3) is \(n(U)=5\)

Step2: Calculate the odds in favor

The odds in favor of an event \(E\) is given by \(\frac{n(F)}{n(U)}\). So the odds in favor of rolling a 3 is \(\frac{1}{5}\)

Answer:

1. D. 24
2. C. \(\frac{3}{8}\)
3. B. \(\frac{1}{5}\)