two six - sided dice are tossed. event a: the first die does not land on 1. event b: the second die does not…

two six - sided dice are tossed. event a: the first die does not land on 1. event b: the second die does not land on 6. 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 does not land on 1. event b: the second die does not land on 6. 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: Calculate P(A)

The first die has 6 possible outcomes. The number of outcomes where it does not land on 1 is 5. So $P(A)=\frac{5}{6}$.

Step2: Calculate P(B)

The second die has 6 possible outcomes. The number of outcomes where it does not land on 6 is 5. So $P(B)=\frac{5}{6}$.

Step3: Calculate P(A and B)

Since A and B are independent events, we use the formula $P(A\text{ and }B)=P(A)\cdot P(B)$. Substitute $P(A)=\frac{5}{6}$ and $P(B)=\frac{5}{6}$ into the formula: $P(A\text{ and }B)=\frac{5}{6}\times\frac{5}{6}=\frac{25}{36}$.

Answer:

$\frac{25}{36}$