Randy is playing a game using two spinners. He will spin each spinner once and will move forward or backward on a game board according to the results of the spins.

Question

Information
Short description, A diagram shows the two spinners.,Long description,
The first spinner is divided into two equal parts, labeled forward and backward. The second spinner is divided into 3 equal parts, labeled 1 Step, 2 Steps, 3 steps.
Question
What is the probability Randy will have to move more than one step forward?

Answer 1

To calculate the probability that Randy will have to move more than one step forward, we first need to analyze the outcomes of both spinners.

1. First Spinner:

   • It has 2 sections: Forward (F) and Backward (B).
   • Probability of landing on Forward (P(F)) = 1/2
   • Probability of landing on Backward (P(B)) = 1/2

2. Second Spinner:

   • It has 3 sections: 1 Step, 2 Steps, and 3 Steps.
   • Probability of landing on 1 Step (P(1)) = 1/3
   • Probability of landing on 2 Steps (P(2)) = 1/3
   • Probability of landing on 3 Steps (P(3)) = 1/3

To move more than one step forward, Randy can achieve that in the following scenarios:

Scenario 1: Forward with 2 Steps

• P(F) * P(2) = (1/2) * (1/3) = 1/6

Scenario 2: Forward with 3 Steps

• P(F) * P(3) = (1/2) * (1/3) = 1/6

Total Probability of Moving More than One Step Forward

Now we add the probabilities from both scenarios: \[ P(\text{More than 1 Step Forward}) = P(\text{Forward with 2 Steps}) + P(\text{Forward with 3 Steps}) = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3} \]

Thus, the probability that Randy will have to move more than one step forward is \(\frac{1}{3}\).