Question

finding the probability of independent events
if miranda flips a coin twice, what is the probability that both coins will land heads up?
the probability that the first coin will land heads up is
the probability that the second coin will land heads up is
the probability that both coins will land heads up is
1/8
1/4
1/2
3/4

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 $\frac{1}{4}$.