A spinner with three equal spaces (labeled A,B, and C) is spun. If the spinner lands on A or C a coin is flipped. If the spinner lands on B a standard 6-sided dice is rolled. What is the probability of spinning a B and rolling a prime?

Prob(B) = 1/3

prob(prime) = 3/6 = 1/2

Prob(B, then a prime) = (1/3)(1/2) = 1/6

To find the probability of spinning a B and rolling a prime, we need to consider the possible outcomes and calculate the favorable outcomes.

First, let's list the possible outcomes for spinning the spinner:
- Spinner lands on A: Coin flip (Heads or Tails)
- Spinner lands on B: Dice roll (1, 2, 3, 4, 5, or 6)
- Spinner lands on C: Coin flip (Heads or Tails)

Since we're interested in the probability of spinning a B and rolling a prime number, let's list the favorable outcomes:
- Spinner lands on B: Dice rolls a prime number (2, 3, or 5)

Now, let's calculate the probability:

1. Probability of spinning a B: Since there are three equal spaces (A, B, and C), each labeled one-third of the spinner, the probability of spinning a B is 1/3.

2. Probability of rolling a prime: Out of the six possible outcomes of rolling a standard 6-sided dice, there are three prime numbers (2, 3, and 5). So, the probability of rolling a prime is 3/6 or simplified to 1/2.

To find the probability of both events occurring, we multiply the probabilities of each event:

Probability of spinning a B and rolling a prime = Probability of spinning a B * Probability of rolling a prime
= (1/3) * (1/2)
= 1/6

Therefore, the probability of spinning a B and rolling a prime is 1/6.