A human gene carries a certain disease from the mother to the child with a probability rate of 53%. That is,
there is a 53% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has
three children. Assume that the infections of the three children are independent of one another. Find the
probability that all three of the children get the disease from their mother.
I don't really need an answer persay. I am trying to figure out a formula or how to figure out this problem for the most part because I am confused!
pr= .53*.53*.53
mother wants to divide $680.00 among her children according to the ratio 2:4:6. The shares would be
To find the probability that all three children get the disease from their mother, you can multiply the probabilities of each child getting the disease independently.
Given that the probability of a child getting the disease is 53% (0.53):
The probability that the first child gets the disease is 0.53.
The probability that the second child gets the disease is also 0.53.
The probability that the third child gets the disease is also 0.53.
Since the infections of the three children are assumed to be independent, you can multiply these probabilities together:
Probability of all three children getting the disease = 0.53 * 0.53 * 0.53 = 0.53^3
Therefore, the probability that all three children get the disease from their mother is 0.53 raised to the power of 3.
To solve this problem, we can use the concept of independent events. Since the infections of the three children are independent of each other, we can multiply the probabilities of each individual event to find the probability of all three children getting the disease.
Let's break down the problem step by step:
Step 1: Determine the probability that a single child gets the disease from their mother. In this case, the probability is given as 53% or 0.53.
Step 2: Since the infections of the three children are independent, we can multiply the probabilities together. To find the probability that all three children get the disease, we multiply the probability for each child. Therefore, the probability of all three children getting the disease is:
0.53 * 0.53 * 0.53 = 0.53^3 ≈ 0.1489
So, the probability that all three children get the disease from their mother is approximately 0.1489 or 14.89%.
In general, if you have n independent events with the same probability p, you can find the probability that all n events occur by multiplying p by itself n times, or p^n.