Question

two six-sided dice are tossed.
event a: the first die does not land on 5.
event b: the second die lands on 4.

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 Complementary Probability knowledge point

$$ P(A) = 1 - \frac{1}{6} = \frac{5}{6} $$

Calculate the probability of Event B

Using the Theoretical Probability knowledge point

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

Calculate the joint probability of both events

Using the Independent Events knowledge point

$$ P(A \text{ and } B) = P(A) \cdot P(B) = \frac{5}{6} \cdot \frac{1}{6} = \frac{5}{36} $$

Convert the probability to a percentage

Using the Relative Frequency knowledge point

$$ \frac{5}{36} \approx 0.13888... \approx 14\% $$

Answer:

Two six-sided dice are tossed.
Event A: The first die does NOT land on 5.
Event B: The second die lands on 4.
What is the probability that both events will occur?
\(P(A \text{ and } B) =\) <blank>14</blank>%