A parent’s chance of passing a rare inherited disease on to a child is 0.15. What is the probability that, in a family of three children, none of the children inherits the disease from the parent?
.85 * .85 * .85 = ?
To find the probability that none of the children inherits the disease from the parent, we need to determine the probability that each child does not inherit the disease and then multiply those probabilities together.
Given that the parent's chance of passing the disease on to a child is 0.15, the probability that a child does not inherit the disease would be 1 - 0.15 = 0.85.
Now, since there are three children in the family, we need to calculate the cumulative probability that all three children do not inherit the disease.
To do this, we multiply the probabilities together:
P(none of the children inherit the disease) = P(child 1 does not inherit the disease) x P(child 2 does not inherit the disease) x P(child 3 does not inherit the disease)
P(none of the children inherit the disease) = 0.85 x 0.85 x 0.85
Simplifying the calculation:
P(none of the children inherit the disease) = 0.85^3
Using a calculator, we find:
P(none of the children inherit the disease) ≈ 0.614
Therefore, the probability that none of the three children inherits the disease from the parent is approximately 0.614 or 61.4%.