A husband and wife discover that there is a 10% probability of their passing on a hereditary disease to any child they have. If they plan to have three children, what is the probability of the event that at least one child will inherit the disease?
1-.1=.9
(.9)^3 =.729
1-.729= .271 or 27.1%
Well, let me calculate that for you with a dash of clown humor. But first, I must put on my clown glasses. 🤡 Alrighty, let's get down to the mathy business!
The probability of passing on the disease to a child is 10%. So, the probability of the child not inheriting the disease is 90% (100% - 10%).
Now, let's calculate the probability of all three children not inheriting the disease. It's just multiplying the probabilities together: 90% x 90% x 90% = 72.9%.
But we want the probability of at least one child inheriting the disease. So, to calculate that, we subtract the probability of none of the children inheriting the disease from 100%: 100% - 72.9% = 27.1%.
Therefore, the probability of at least one child inheriting the disease is 27.1%. But remember, humor is the best medicine, so let's keep spreading laughter along the way! 🤡💙
To find the probability that at least one child will inherit the disease, we need to consider the complement of the event that none of the children inherit the disease.
The probability that any individual child does not inherit the disease is 1 - 0.10 = 0.90.
Since the children are independent events, the probability that none of the three children inherit the disease is calculated by multiplying the probabilities together: 0.90 * 0.90 * 0.90 = 0.729.
Therefore, the probability that at least one child will inherit the disease is 1 - 0.729 = 0.271, or 27.1%.
To calculate the probability of at least one child inheriting the disease, we can use the concept of complementary probability. We'll find the probability of none of the children inheriting the disease and then subtract it from 1 to get the desired probability.
Let's break it down step by step:
1. Find the probability of a child not inheriting the disease: Since the disease has a 10% probability of being passed on, the probability of any child not inheriting it would be 1 - 0.10 = 0.90 (90%).
2. Calculate the probability of none of the three children inheriting the disease: Since each child is an independent event, we can multiply their probabilities together. So, the probability of none of the three children inheriting the disease would be 0.90 * 0.90 * 0.90 = 0.729 (72.9%).
3. Calculate the probability of at least one child inheriting the disease: Now, we can subtract the probability of none of the children inheriting the disease from 1. So, the probability of at least one child inheriting the disease is 1 - 0.729 = 0.271 (27.1%).
Therefore, the probability that at least one child will inherit the disease is 0.271 or 27.1%.