SOLUTION: Let x determine a random​ variable, and use your knowledge of probability to prepare a probability distribution.
A family has tow children and the number of girls is recorded.â€
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Question 1193967: Let x determine a random​ variable, and use your knowledge of probability to prepare a probability distribution.
A family has tow children and the number of girls is recorded.​ (Assume an equal chance of a boy or girl for each​ birth.)
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
X = number of girls
Since the family has 2 kids, this means X can be either
X = 0
X = 1
X = 2
Of course, only one outcome is possible.
If X = 0, then the family has 0 girls and 2 boys
1/2 is the probability of getting a boy
(1/2)*(1/2) = 1/4 is the probability of two boys. Each birth is independent.
So P(X) = 1/4 when X = 0
Through symmetry, we'll find that P(X) = 1/4 when X = 2
This works simply because the probability of either gender is the same (i.e. each gender is equally likely).
If X = 1, then the family has 1 girl and 1 boy
(1/2)*(1/2) = 1/4 is the probability of getting a girl followed by a boy
1/4 is also the probability of getting a boy followed by a girl
1/4 + 1/4 = 1/2 is the probability of getting a boy and a girl in either order.
P(X) = 1/2 when X = 1
Here's what the probability distribution looks like in a table format.Where X is the number of girls.
Notice that all of the P(X) values are on the interval
Furthermore notice that the sum of the P(X) values leads to 1 (to represent 100% of all possible cases).
Optionally if you wanted to, you can convert the fractions to decimal form
1/4 = 0.25
1/2 = 0.5
Usually I like to keep the fractions because they are exact compared to decimal counterparts. In this case, both 0.5 and 0.25 are exact, so it's up to you which version you prefer. Be sure to follow any instructions provided by the teacher.
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