Question

Select the statements that are true based on the following given information.

D={xl xis a whole number)
E = {x\ x is a perfect square < 36)
F=(x1 x is an even number between 20 and 30)

Answer 1

The term P(EM) refers to the probability of rolling a number that is both even and a multiple of three, which on a six-sided die, corresponds to the number 6. P(E OR M) represents the probability of rolling either an even number or a multiple of three, which include the numbers 2, 3, 4, and 6 on a six-sided die.

Step-by-step explanation:

The questions pertain to probability theory, a branch of mathematics focused on the analysis of random events. When asked about P(EM), it is referring to the probability that two events, E and M, occur simultaneously on a fair six-sided cube. In this context, E is the event of rolling an even number, and M is the event of rolling a multiple of three.

The term P(E OR M) signifies the probability that either event E or event M, or both, occur. It is essential to consider that some numbers may satisfy both criteria, being both even and multiples of three.

To illustrate, let's consider a six-sided die with faces 1 through 6. The even numbers are 2, 4, and 6, while the multiples of three are 3 and 6. Therefore, the P(EM) corresponds to the event of landing on 6, seeing as it is the only number that is both even and a multiple of three. On the other hand, P(E OR M) includes all the possible outcomes that are either even numbers or multiples of three, which are 2, 3, 4, and 6.