To find the probability that both events A and B occur, we first need to determine the individual probabilities of each event.
1. Probability of Event A (coin lands on heads):
- A standard coin has two sides: heads and tails.
- The probability of the coin landing on heads is therefore:
[tex]\[
P(A) = \frac{1}{2}
\][/tex]
2. Probability of Event B (die lands on 1, 3, or 6):
- A standard six-sided die has six faces, numbered 1 through 6.
- The favorable outcomes for event B are the die landing on 1, 3, or 6.
- There are 3 favorable outcomes out of the 6 possible outcomes, so the probability of the die landing on 1, 3, or 6 is:
[tex]\[
P(B) = \frac{3}{6} = \frac{1}{2}
\][/tex]
3. Probability of both events A and B occurring:
- Since events A and B are independent (the outcome of the coin toss does not affect the outcome of the die roll), we can use the formula for the probability of independent events both occurring:
[tex]\[
P(A \text{ and } B) = P(A) \cdot P(B)
\][/tex]
Putting the calculated probabilities into the formula, we get:
[tex]\[
P(A \text{ and } B) = \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}
\][/tex]
So, the probability that both events will occur is:
[tex]\[
P(A \text{ and } B) = \frac{1}{4}
\][/tex]
In decimal form, this is 0.25.
