Question

What is the probability that both events will occur? First, find the probability of event A.

Two dice are rolled.
Event A: The first die is a 4 or less.
Event B: The second die is even.
P(A)= [?]
Enter as a decimal rounded to the nearest hundredth.

Answer 1

Step-by-step explanation:"To find the probability of event A, you can count the number of outcomes where the first die is a 4 or less. There are 4 possible outcomes out of 6, so the probability of event A is 4/6, or 2/3. To find the probability that both events A and B will occur, you can multiply the probabilities of each event. The probability of event B is 1/2, since there are 3 even numbers out of 6 possible outcomes. Therefore, the probability of both events A and B occurring is (2/3) * (1/2), or 1/3. This can be written as 0.33 when rounded to the nearest hundredth. Does that help?"

Answer 2

The probability of event A is approximately 0.67.

To find the probability of event A, which is the probability that the first die rolled is a 4 or less, we consider that a standard die has six faces, numbered from 1 to 6.

Since event A includes the outcomes where the first die shows a 1, 2, 3, or 4, there are 4 favorable outcomes out of 6 possible outcomes when rolling one die.

The probability of event A (P(A)) is calculated as the number of favorable outcomes divided by the total number of possible outcomes:

`\[ P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]`

`\[ P(A) = (4)/(6) \]`

This fraction can be simplified to:

`\[ P(A) = (2)/(3) \]`

Now, to express this as a decimal rounded to the nearest hundredth, we perform the division:

`\[ P(A) = (2)/(3) \approx 0.6667 \]`

Rounded to the nearest hundredth:

`\[ P(A) \approx 0.67 \]`

So, the probability of event A is approximately 0.67.