Question

determine the probability in each situation. express your answers as fractions in lowest terms.
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?
$p(\text{par}, \text{par}) = \frac{2}{3} \cdot \frac{2}{3} = \frac{4}{9}$
clarence rolls 2 number cubes, numbered 1–6. what is the probability that he will roll a number greater than 4 on both rolls?

enter the answer in the space provided. use numbers instead of words.

Explanation:

For Malcolm's golf problem:

Step1: Identify the probability for one hole

The probability of Malcolm making a par on one hole is $\frac{2}{3}$.

Step2: Calculate the probability for two independent holes

Since the two holes are independent events, we multiply the probabilities. So, $P(\text{par on both holes}) = \frac{2}{3} \times \frac{2}{3}$.

Step3: Simplify the product

$\frac{2}{3} \times \frac{2}{3} = \frac{4}{9}$.

Step1: Find the probability for one roll

A number cube has numbers 1 - 6. Numbers greater than 4 are 5 and 6, so there are 2 favorable outcomes. The probability of rolling a number greater than 4 on one roll is $\frac{2}{6}=\frac{1}{3}$.

Step2: Calculate the probability for two independent rolls

Since the two rolls are independent, we multiply the probabilities. So, $P(\text{greater than 4 on both rolls})=\frac{1}{3}\times\frac{1}{3}$.

Step3: Simplify the product

$\frac{1}{3}\times\frac{1}{3}=\frac{1}{9}$.

Answer:

$\frac{4}{9}$

For Clarence's number cube problem (assuming the question is "What is the probability that he will roll a number greater than 4 on both rolls?"):