sam and erica are playing a board game. they spin a pointer to determine whether to move forward or back…

sam and erica are playing a board game. they spin a pointer to determine whether to move forward or back. they toss a number cube to determine how many spaces to move. what is the probability of moving forward an even number of spaces?

sam and erica are playing a board game. they spin a pointer to determine whether to move forward or back. they toss a number cube to determine how many spaces to move. what is the probability of moving forward an even number of spaces?

Answer

Explanation:

Step1: Determine probability of moving forward

The spinner is divided into 2 equal - parts (move forward and move back), so the probability of moving forward, $P(F)=\frac{1}{2}$.

Step2: Determine probability of getting an even number on the number - cube

A standard number cube has 6 faces numbered 1 - 6. The even numbers are 2, 4, 6. So the probability of getting an even number on the number cube, $P(E)=\frac{3}{6}=\frac{1}{2}$.

Step3: Use the multiplication rule for independent events

Since spinning the pointer and tossing the number cube are independent events, the probability of moving forward and moving an even number of spaces is $P = P(F)\times P(E)$. $P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$

Answer:

$\frac{1}{4}$