The probability that a person owns a microwave oven is .75, that a person owns a compact disk player is .25, and that a person owns both a microwave and a CD player is .16. Find the probability that a person owns either a microwave or a CD player, but not both.

p(not having both)=0.84

=0.84-0.16
=0.68

To find the probability that a person owns either a microwave or a CD player, but not both, we need to subtract the probability that a person owns both from the sum of the probabilities that a person owns a microwave and a CD player separately.

Let's call the probability that a person owns a microwave M and the probability that a person owns a CD player C.

Given:
P(M) = 0.75 (probability a person owns a microwave)
P(C) = 0.25 (probability a person owns a CD player)
P(M∩C) = 0.16 (probability a person owns both a microwave and a CD player)

To find the probability that a person owns either a microwave or a CD player, but not both, we can use the formula:

P(A∪B) = P(A) + P(B) - 2(P(A∩B))

In this case, A represents owning a microwave, and B represents owning a CD player.

Substituting the given values into the formula:

P(A∪B) = P(M) + P(C) - 2(P(M∩C))
P(A∪B) = 0.75 + 0.25 - 2(0.16)
P(A∪B) = 0.75 + 0.25 - 0.32
P(A∪B) = 0.93

Therefore, the probability that a person owns either a microwave or a CD player, but not both, is 0.93 or 93%.

To find the probability that a person owns either a microwave or a CD player, but not both, we can use the principle of inclusion-exclusion.

Let's define the following events:
A: A person owns a microwave oven
B: A person owns a compact disk player

We are given the following probabilities:
P(A) = 0.75 (Probability that a person owns a microwave oven)
P(B) = 0.25 (Probability that a person owns a CD player)
P(A ∩ B) = 0.16 (Probability that a person owns both a microwave and a CD player)

The probability that a person owns either a microwave or a CD player, but not both, is given by the expression P((A ∪ B) - (A ∩ B)).

To calculate this, we need to calculate P(A ∪ B) and P(A ∩ B).

Using the principle of inclusion-exclusion, we have:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Plugging in the given probabilities:
P(A ∪ B) = 0.75 + 0.25 - 0.16
P(A ∪ B) = 0.84

Now, we need to calculate P(A ∩ B):
P(A ∩ B) = 0.16 (Given)

Finally, we can calculate the probability that a person owns either a microwave or a CD player, but not both:
P((A ∪ B) - (A ∩ B)) = P(A ∪ B) - P(A ∩ B)
P((A ∪ B) - (A ∩ B)) = 0.84 - 0.16
P((A ∪ B) - (A ∩ B)) = 0.68

Therefore, the probability that a person owns either a microwave or a CD player, but not both, is 0.68.

0.75+0.25-0.16=0.84