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?
How does that work?
The chance of a child NOT having the inhertited disease is 0.85. For none of the three children to get it, the probability is 0.85^3 = 0.614
To find the probability that none of the children inherit the disease from the parent, we can use the concept of independent events. The probability that a child does not inherit the disease from the parent is given as 1 minus the probability that the child does inherit the disease, which is 1 - 0.15 = 0.85.
Since the events of each child inheriting or not inheriting the disease are independent, we can multiply the probabilities together to find the probability that all three children do not inherit the disease:
Probability that 1st child does not inherit the disease = 0.85
Probability that 2nd child does not inherit the disease = 0.85
Probability that 3rd child does not inherit the disease = 0.85
Probability that none of the three children inherit the disease = 0.85 * 0.85 * 0.85 = 0.614
Therefore, the probability that in a family of three children, none of the children inherits the disease from the parent is 0.614 or approximately 61.4%.