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If the probability that a hygienist likes dental floss is 0.55, the probability of those who like both dental floss and water picks is 0.33, and the probability of those who like neither is 0.05, what is the probability of those who like only water picks

Respuesta :

The probability of those who like only water picks is 0.73.

What is probability ?

Probability refers to the chance of occurrence of an event.

Let E be an event and P(E) be the probability of its occurrence.

Then, P(E) = [tex]\frac{Number Of Favorable Outcomes Of E}{Total Number Of Outcomes}[/tex]

Given:

  1. P(Hygienists like dental floss) = 0.55
  2. P(Hygienists like both dental floss and water picks) = 0.33
  3. P(Hygienists like neither dental floss and water picks) = 0.05

Now, let:

  1. A = Hygienists who like dental floss
  2. B = Hygienists who like water picks

Then,

  1. P(A) = ? (let x)
  2. P(B) = 0.55
  3. P(A∩B) = 0.33
  4. P(A'∩B') = 0.05

Now, we know that P(A'∩B') = P((A∪B)') = 1 - P(A∪B)

Thus, 0.05 = 1 - P(A∪B)

=> P(A∪B) = 1 - 0.05 = 0.95

Also, P(A∪B) = P(A) + P(B) - P(A∩B)

Therefore, 0.95 = x + 0.55 - 0.33

=> x = 0.95 - 0.22 = 0.73

Thus, the probability of those who like only water picks is 0.73.

To learn more about probability  from the given link:

https://brainly.com/question/13604758

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