Question

two six-sided dice are tossed.
event a: the first die lands on 1, 2, 3, or 4.
event b: the second die lands on 3, 4, 5, or 6.

what is the probability that both events will occur?

\\(p(a \text{ and } b) = ?\\%\\)

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

$$ P(A) = \frac{4}{6} = \frac{2}{3} $$

Calculate the probability of Event B

Using the Theoretical Probability knowledge point

$$ P(B) = \frac{4}{6} = \frac{2}{3} $$

Calculate the joint probability

Using the Independent Events and Probability of Intersection knowledge points

$$ P(A \text{ and } B) = P(A) \cdot P(B) = \frac{2}{3} \cdot \frac{2}{3} = \frac{4}{9} $$

Convert the probability to a percentage

Using the Theoretical Probability knowledge point

$$ \frac{4}{9} \approx 0.4444 = 44.44\% \approx 44\% $$

Answer:

Two six-sided dice are tossed.
Event A: The first die lands on 1, 2, 3, or 4.
Event B: The second die lands on 3, 4, 5, or 6.
What is the probability that both events will occur?
\(P(A \text{ and } B) =\) <blank>44</blank>%