Question

A board game uses a fair six-sided die and a spinner with five equal-sized sections colored dark blue, green, light blue, red, and yellow. Players roll the die and then spin the spinner. Match each probability statement to its correct value.

A) P(rolling a 3 and spinning red) = 1/30
B) P(rolling a 6 or spinning green) = 1/3
C) P(rolling an even number) = 1/2
D) P(rolling a 1 or spinning yellow) = 1/12

Answer 1

The probability of various events in a board game are calculated by multiplying or adding the probabilities of the individual events. For example, the probability of rolling a 3 and spinning red is 1/30, while the probability of rolling a 6 or spinning green is 1/3.

Step-by-step explanation:

The probability of an event is determined by dividing the number of favorable outcomes by the total number of possible outcomes. Let's match each probability statement with its correct value:

A) P(rolling a 3 and spinning red) = 1/30 – There is a 1/6 probability of rolling a 3, and a 1/5 probability of spinning red. Multiply these probabilities together: (1/6) * (1/5) = 1/30.

B) P(rolling a 6 or spinning green) = 1/3 – There is a 1/6 probability of rolling a 6, and a 1/5 probability of spinning green. Since these events are mutually exclusive, we add the probabilities together: (1/6) + (1/5) = 11/30.

C) P(rolling an even number) = 1/2 – There are three even numbers (2, 4, and 6) out of six possible outcomes, so the probability is 3/6, which simplifies to 1/2.

D) P(rolling a 1 or spinning yellow) = 1/12 – There is a 1/6 probability of rolling a 1, and a 1/5 probability of spinning yellow. Since these events are mutually exclusive, we add the probabilities together: (1/6) + (1/5) = 11/30.