SOLUTION: Suppose that a family has five children, consisting of three girls and two boys. Call the girls Abigail, Brianna, and Courtney; call the boys Duane and Evan. Suppose further that t
Algebra ->
Probability-and-statistics
-> SOLUTION: Suppose that a family has five children, consisting of three girls and two boys. Call the girls Abigail, Brianna, and Courtney; call the boys Duane and Evan. Suppose further that t
Log On
Question 926819: Suppose that a family has five children, consisting of three girls and two boys. Call the girls Abigail, Brianna, and Courtney; call the boys Duane and Evan. Suppose further that two of these children are to be selected at random.
2. Determine the probability that one child of each gender will be selected.
Hi
five children: 3G, 2B
probability that one child of each gender will be selected
.........
P(one girl and one boy) = P(girl first) + P(girl 2nd) = = 3/5
You can put this solution on YOUR website! 3 girls and 2 boys
probability of one child of each gender being selected is:
(3C1 * 2C1) / 5C2
which is equal to 6/10 = 3/5.
probability of picking a girl on the first try and a boy on the second try is equal to 3/5 * 2/4 = 6/20.
probability of picking a boy on the first try and a girl on the second try is equal to 2/5 * 3/4 = 6/20.
since these are independent events, probability of picking a girl on the first try and a boy on the second try or a boy on the first try and a girl on the second try is equal to 6/20 + 6/20 which is equal to 12/20 which simplifies to 3/5.
same answer either way.
3C1 is the number of ways of getting 1 girl out of 3.
2C1 is the number of ways of getting 1 boy out of 2.
5C2 is the number of ways of getting 2 chilcren out of 5.
