Question

sample problem on average, malcolm makes a par on \\(\frac{2}{3}\\) of the golf holes that he plays. what is the probability that he will make a par on each of the next 2 holes that he plays? \\(p(\text{par}, \text{par}) = \frac{2}{3} \cdot \frac{2}{3} = \frac{4}{9}\\) the probability that malcolm makes a par on the next 2 holes is \\(\frac{4}{9}\\). on average, 3 out of 4 students order spaghetti at the cafeteria when it is on the menu. what is the probability that the first 2 students in line for lunch will have spaghetti if it is on the menu? > enter the answer in the space provided. use numbers instead of words.

Explanation:

Step1: Identify the probability for one student

The probability that a single student orders spaghetti is $\frac{3}{4}$ since 3 out of 4 students order it.

Step2: Calculate the probability for two independent events

Since the choices of the two students are independent, we multiply the probabilities. So for the first two students, the probability is $\frac{3}{4} \times \frac{3}{4}$.

Step3: Compute the product

$\frac{3}{4} \times \frac{3}{4} = \frac{3\times3}{4\times4} = \frac{9}{16}$

Answer:

$\frac{9}{16}$