two coins are tossed. event a: the first coin does not land on tails. event b: the second coin does land on…

two coins are tossed. event a: the first coin does not land on tails. event b: the second coin does land on heads. 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 coins are tossed. event a: the first coin does not land on tails. event b: the second coin does land on heads. 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)

When tossing a coin, the probability of getting heads (not tails) for the first - coin. Since there are 2 possible outcomes (heads or tails) and 1 favorable outcome (heads), $P(A)=\frac{1}{2}$.

Step2: Calculate P(B)

When tossing a coin, the probability of getting heads for the second coin. Since there are 2 possible outcomes (heads or tails) and 1 favorable outcome (heads), $P(B)=\frac{1}{2}$.

Step3: Calculate P(A and B)

Since A and B are independent events, we use the formula $P(A\ and\ B)=P(A)\cdot P(B)$. Substitute $P(A)=\frac{1}{2}$ and $P(B)=\frac{1}{2}$ into the formula: $P(A\ and\ B)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$