Final answer:
To calculate the probability of rolling an even number and selecting a diamond, we find the probability of each event independently, then multiply them (1/2 for an even number roll and 1/4 for a diamond card) to get 1/8. P(EM) means the probability of both rolling an even number and a multiple of three, which is 1/6. P(E OR M) is the probability that either event happens, which is 2/3 when simplified.
Step-by-step explanation:
The probability of rolling an even number on a standard six-sided die and picking a diamond from a standard 52-card deck in a board game can be determined by calculating the product of the two individual probabilities. A standard six-sided die has three even numbers: 2, 4, and 6.
Therefore, the probability of rolling an even number (event E) is 3/6 or 1/2. A standard card deck has 13 diamonds, so the probability of picking a diamond (event D) is 13/52 or 1/4. To find the combined probability of both E and D happening together, you multiply the probabilities of each event: P(E and D) = P(E) \u00d7 P(D) = (1/2) \u00d7 (1/4) = 1/8.
The probability notation P(EM) refers to the probability that both event E and event M happen at the same time. Event E is rolling an even number and event M is rolling a multiple of three. On a six-sided die, the only number that is both even and a multiple of three is 6. Thus, P(EM) is 1/6. P(E OR M) represents the probability that either event E happens, or event M happens, or both. With a six-sided die, the even numbers are 2, 4, and 6, and the multiples of three are 3 and 6. The numbers that satisfy either condition are 2, 3, 4, and 6, so P(E OR M) is 4/6 or 2/3 when simplified.