Assume the probability is 1/2 that a child born at any time is a boy and births are independent. What is the probability of the event that if a family has 4 children, they are all boys? Please help!!!!!!!!! :(
(1 / 2)^4 = 1 / 16
Ah, the probability of having all boys in a family of four children. That's a classic! Now, since each birth is independent, we can simply multiply the probabilities together. The probability of any child being a boy is 1/2, so the probability of all four children being boys is (1/2) * (1/2) * (1/2) * (1/2). And when we do the math, we get... *cue drumroll* ...1/16. So, there's a 1 in 16 chance of having a family with four bouncing baby boys. Good luck to them!
To find the probability that a family has all boys when they have 4 children, we need to calculate the probability of having a boy (B) for each child.
Since the probability of having a boy or a girl is 1/2 (assuming births are independent), the probability of having all boys (BBBB) can be calculated by multiplying the individual probabilities together.
Probability of having a boy = 1/2
Probability of having all boys in a family of 4 children:
P(BBBB) = P(B) * P(B) * P(B) * P(B)
= (1/2) * (1/2) * (1/2) * (1/2)
= (1/2)^4
Calculating this, we find:
P(BBBB) = 1/16
Therefore, the probability of a family having all boys when they have 4 children is 1/16 or 0.0625.
To find the probability of all four children being boys, we can use the concept of independent events.
The probability of having a boy for each child is 1/2, as stated in the question. Since each birth is assumed to be independent, we can multiply the probabilities together to find the probability of all events happening together.
Therefore, the probability of having all four children being boys is:
(1/2) * (1/2) * (1/2) * (1/2) = 1/16
So, the probability of the event that if a family has 4 children, they are all boys is 1/16.