Question

three siblings, peyton, cameron, and dakota, all ask their parents to borrow the family car for different events around town. since they cannot all borrow the car at the same time, the parents decide to use randomness to decide who gets the car. they will roll a single, fair, six - sided number cube. peyton gets the car if a 1 or 2 is rolled. cameron gets the car if a 3 or 4 is rolled, and dakota gets the car if a 5 or 6 is rolled. which of the following is the probability distribution for who gets the car?

Explanation:

Step1: Calculate the probability for each sibling

The total number of outcomes when rolling a six - sided number cube is \(n = 6\).
For Peyton: The favorable outcomes (rolling a 1 or 2) are \(m_{1}=2\). Using the probability formula \(P=\frac{m}{n}\), \(P(\text{Peyton})=\frac{2}{6}=\frac{1}{3}\).
For Cameron: The favorable outcomes (rolling a 3 or 4) are \(m_{2} = 2\). Using the probability formula \(P=\frac{m}{n}\), \(P(\text{Cameron})=\frac{2}{6}=\frac{1}{3}\).
For Dakota: The favorable outcomes (rolling a 5 or 6) are \(m_{3}=2\). Using the probability formula \(P=\frac{m}{n}\), \(P(\text{Dakota})=\frac{2}{6}=\frac{1}{3}\).

Answer:

Peyton: \(\frac{1}{3}\), Cameron: \(\frac{1}{3}\), Dakota: \(\frac{1}{3}\) (the second option in the given choices)