Suppose you conduct a study and find that the probability of having a baby boy is 60%. Now suppose three of your relatives are going to have babies.
a) Build a tree diagram showing all the conditional probabilities and joint probabilities associated with the sex of the three new babies.
b) What rule of probability are you using to obtain the joint probabilities and why? In order to answer the “why” part of the question you must tell me why the rule of probability you chose to use applies in this case.
c) What is the probability of having one boy and two girls in the three births?
Please repost with completed question. Thanks for asking.
binomial
p(r) = C(n,r) p^(r) (1-p)^(n-r)
here n = 3 , p=.6 (boy), (1-p)=.4 (girl)
p(0 boys) = 1*.6^0* .4^3 = .064
p(1 boy ) = 3 *.6^(1) *.4^2 = .288
p(2 boys) = 3*.6^2*.4^1 = .432
p(3 boys) = 1*.6^3*.4^0 = .216
I guess whatever your question might be, that might help.
a) To build a tree diagram showing the conditional and joint probabilities associated with the sex of the three new babies, we first start with the initial probability of having a baby boy, which is 0.6. From there, we consider all possible outcomes for each birth: either a boy (B) or a girl (G).
The tree diagram would look like this:
B (0.6) | G (0.4)
\ /
B (0.6) G (0.4) | B (0.6) G (0.4)
| \ /
B (0.6) G (0.4) | G (0.4) B (0.6) | B (0.6) G (0.4)
| |
--------------
| | |
B (0.6) G (0.4) | B (0.6) G (0.4)
In this tree diagram, each branch represents the probability of each possible outcome at each birth, and the numbers on each branch indicate the corresponding probabilities.
b) In order to obtain the joint probabilities, we are using the multiplication rule of probability. The multiplication rule states that the probability of two or more independent events occurring together is equal to the product of their individual probabilities.
In this case, we are assuming that the births are independent events, meaning that the outcome of one birth does not influence the outcome of another. Therefore, we can use the multiplication rule to calculate the joint probabilities by multiplying the probabilities along the corresponding branches in the tree diagram.
The multiplication rule applies in this case because the probability of having a baby boy for each birth remains constant (0.6) and is assumed to be independent of the other births.
c) To find the probability of having one boy and two girls in the three births, we need to consider the different possible combinations of births that satisfy this condition.
From the tree diagram, we can see three such combinations: BGG, GBG, and GGB. The probabilities associated with each combination can be obtained by multiplying the probabilities along the branches of the tree diagram for each birth.
For example, the probability of the combination BGG is 0.6 * 0.4 * 0.4 = 0.096.
Similarly, we can calculate the probabilities for the other two combinations: GBG and GGB.
Finally, we can find the total probability of having one boy and two girls by summing up the probabilities of all three combinations: 0.096 + 0.096 + 0.096 = 0.288, or 28.8%.
Therefore, the probability of having one boy and two girls in the three births is 28.8%.