Question

a coin and a six-sided die are tossed.
event a: the coin lands on heads.
event b: the die lands on 1, 3, or 6.
what is the probability that both events will occur?
\\(p(a \text{ and } b) = \quad\\%\\)
for independent events: \\(p(a \text{ and } b) = p(a) \cdot p(b)\\)
round your answer to the nearest whole percent.

Explanation:

Calculate the probability of Event A

Using the Theoretical Probability knowledge point

$$ P(A) = \frac{1}{2} = 0.5 $$

Calculate the probability of Event B

Using the Theoretical Probability knowledge point

$$ P(B) = \frac{3}{6} = \frac{1}{2} = 0.5 $$

Calculate the joint probability of both events

Using the Independent Events and Probability of Intersection knowledge points

$$ P(A \text{ and } B) = P(A) \cdot P(B) = 0.5 \cdot 0.5 = 0.25 $$

Convert the probability to a percentage

Using the Theoretical Probability knowledge point

$$ 0.25 \times 100\% = 25\% $$

Answer:

A coin and a six-sided die are tossed.
Event A: The coin lands on heads.
Event B: The die lands on 1, 3, or 6.

What is the probability that both events will occur?

\(P(A \text{ and } B) =\) <blank>25</blank>%