finding the probability of independent events\nif miranda flips a coin twice, what is the probability that…

Explanation:

Step1: Probability of first - coin head

A fair coin has 2 possible outcomes (head or tail). The probability of getting a head on the first coin flip is $\frac{1}{2}$.

Step2: Probability of second - coin head

Since the coin flips are independent events, the probability of getting a head on the second coin flip is also $\frac{1}{2}$.

Step3: Probability of both heads

For independent events $A$ and $B$, the probability of both $A$ and $B$ occurring is $P(A\cap B)=P(A)\times P(B)$. Here, $A$ is the event of the first - coin landing heads and $B$ is the event of the second - coin landing heads. So $P(A) = \frac{1}{2}$, $P(B)=\frac{1}{2}$, and $P(A\cap B)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

The probability that the first coin will land heads up is $\frac{1}{2}$. The probability that the second coin will land heads up is $\frac{1}{2}$. The probability that both coins will land heads up is $\frac{1}{4}$.