two six - sided dice are tossed. event a: the first die lands on 2. event b: the second die lands on 4. what…

two six - sided dice are tossed. event a: the first die lands on 2. event b: the second die lands on 4. what is the probability that both events will occur? for independent events: p(a and b)=p(a)·p(b) p(a and b)=? give your answer in simplest form.

two six - sided dice are tossed. event a: the first die lands on 2. event b: the second die lands on 4. what is the probability that both events will occur? for independent events: p(a and b)=p(a)·p(b) p(a and b)=? give your answer in simplest form.

Answer

Explanation:

Step1: Find probability of event A

The first die has 6 possible outcomes, and landing on 2 is 1 outcome. So $P(A)=\frac{1}{6}$.

Step2: Find probability of event B

The second die has 6 possible outcomes, and landing on 4 is 1 outcome. So $P(B)=\frac{1}{6}$.

Step3: Calculate $P(A\ and\ B)$

Since A and B are independent events, $P(A\ and\ B)=P(A)\cdot P(B)$. Substitute $P(A)=\frac{1}{6}$ and $P(B)=\frac{1}{6}$ into the formula: $P(A\ and\ B)=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$.

Answer:

$\frac{1}{36}$