In a soft ball gme, Archie getting hit is 1/4. the probability of betty getting hit is 1/4, and Veronica's probability is 1/2 for getting hit. if each goes to bat once, what is the probability that exactly one gets a hit

To find the probability that exactly one person gets a hit, we need to calculate the probability for each person individually and then add those probabilities together.

Let's start with Archie. The probability that Archie gets a hit is 1/4.

Next, we consider Betty. The probability that Betty gets a hit is also 1/4.

Lastly, we have Veronica. The probability that Veronica gets a hit is 1/2.

Since each person goes to bat once, the events of Archie, Betty, and Veronica getting a hit are independent. This means we can multiply their individual probabilities to find the probability of all three events occurring.

The probability of exactly one person getting a hit is the sum of the probabilities that Archie gets a hit but Betty and Veronica do not, plus the probabilities that Betty gets a hit but Archie and Veronica do not, plus the probabilities that Veronica gets a hit but Archie and Betty do not.

Let's calculate it step by step:

Probability(Archie gets a hit) = 1/4
Probability(Betty does not get a hit) = 3/4 (1 - 1/4)
Probability(Veronica does not get a hit) = 1/2 (1 - 1/2)

Now we can calculate the probability that Archie gets a hit but Betty and Veronica do not:

Probability(Archie gets a hit but Betty and Veronica do not) = Probability(Archie gets a hit) * Probability(Betty does not get a hit) * Probability(Veronica does not get a hit)
= (1/4) * (3/4) * (1/2)
= 3/32

Similarly, we calculate the probabilities for Betty and Veronica:

Probability(Betty gets a hit but Archie and Veronica do not) = (1/4) * (3/4) * (1/2) = 3/32
Probability(Veronica gets a hit but Archie and Betty do not) = (1/2) * (3/4) * (1/2) = 3/16

Finally, we add the probabilities together to get the total probability that exactly one person gets a hit:

Probability(Exactly one person gets a hit) = Probability(Archie gets a hit but Betty and Veronica do not) + Probability(Betty gets a hit but Archie and Veronica do not) + Probability(Veronica gets a hit but Archie and Betty do not)
= 3/32 + 3/32 + 3/16
= 9/32

So, the probability that exactly one person gets a hit is 9/32.