Question

A kindergarden class consists of 14 boys and 11 girls. If the teacher selects children a)...

A kindergarden class consists of 14 boys and 11 girls. If the teacher selects children

a) What is the probability that the first selected child will be a girl if the teacher uses random sampling?

b) If the teacher selects a random sample of n=3 children, and the first two children are boys and leave the classroom as soon as selected, what is the probability that the third child selected will be a girl?
c) In the same situation, what is the probability that the third child is a boy?

Homework Answers

Answer #1

kindergarden class consist of 14 boys and 11 girls.

total students in the class = 25

teacher is selecting at random so every student has an equal probability of being selected.and is equal to 1/25, that is all the selections are equally likely with probability 1/25

a.

the probability that the first selected student is a girl

= total no. of girls in the class/total students in the class

=11/25

altrnatively

the probability that the first selected student is a girl = (probabiliy of being selected)* total no of girls=1/25 * 11 = 11/25

______________________________________________

b.

in the random sample of 3,

first two selections are boys and leave the classroom as soon as selected.

it should be noted that since the selection is random, the remaining selection is equally likely,

(with probability=1/23)

since two boys leaved the classroom,

total no of remaining boys =12 and total no. girls remains the same = 11

total students remaining for selection = 23

the probability that the first selected student is a girl = total no. of girls / total students remaining

=11/23

altrnatively

the probability that the third selected student is a girl = (probabiliy of being selected among the remaining students)* total no of girls=1/23 * 11 = 11/23

_____________________________________________________________

c.

in the same above situation,

the probability that the third child is a boy = remaining no. of the boys after two selections/ total students remaining after two selections

=12/23

alternatively

the probability that the third selected student is a boy = (probabiliy of being selected among the remaining students)* remaining no of boys=1/23 * 12 = 1223

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A class consists of 35 girls and 45 boys,9 girls and 17 boys of the class...
A class consists of 35 girls and 45 boys,9 girls and 17 boys of the class take mathematics as their optional subject what is the probability that a student selected at random from the class is a boy or takes mathematics?
A student is chosen at random from a class of 16 girls and 14 boys. What...
A student is chosen at random from a class of 16 girls and 14 boys. What is the probability that the student chosen is a girl?
A high school principal must select 14 girls at random from the freshman class to serve...
A high school principal must select 14 girls at random from the freshman class to serve as hostesses at the junior-senior prom. There are 170 freshman girls, including 10 from minorities, and the principal would like at least one minority girl to have this honor. (Round your answers to two decimal places.) (a) If he selects the girls at random, what is the probability that he will select exactly one minority girl? (b) If he selects the girls at random,...
1. If a couple plans to have 4 children, what is the probability that there will...
1. If a couple plans to have 4 children, what is the probability that there will be at least one girl? Assume boys and girls are equally likely. 2. Find the probability of a couple having a baby boy when their 4th child is born, given that the first three children were all boys. Assume boys and girls are equally likely.
Suppose that a family has five children, consisting of three girls and two boys. Call the...
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. List the sample space of all possible pairs of these five children. a. Determine the probability that one child of each gender will be selected. Report your answer to two decimal places; e.g., 0.xx b. Determine the probability that two...
Boys and Girls: Suppose a couple plans to have two children and the probability of having...
Boys and Girls: Suppose a couple plans to have two children and the probability of having a girl is 0.50. (a) What is the sample space for the gender outcomes? {bb, bg, gb, gg}{bb, bg, gg}    {bb, gg}{b,g} (b) What is the probability that the couple has one boy and one girl? 1 2 3 4       1 4 1 3 (c) What is the probability that the couple will have at least one girl? 1 4 1 2       3...
Tilly’s Daycare School visited a zoo during a pre-school celebration week. A sampling of children was...
Tilly’s Daycare School visited a zoo during a pre-school celebration week. A sampling of children was asked if the zoo were to get one additional animal, would they prefer a lion or an elephant. The results of the survey follow: Lion Elephant Total Boys 90 110 200 Girls 75 85 160 Total 165 195 360 If one child who was in the survey is selected at random, find the probability that: a) The child selected the lion; given the child...
Ms. Frazier chooses two students to come to the board from a class of 8 boys...
Ms. Frazier chooses two students to come to the board from a class of 8 boys and 12 girls. What is the probability that she will select a girl student first and a boy student second?
A class has 10 boys (including Doug) and 8 girls (including Cathy). If 3 students are...
A class has 10 boys (including Doug) and 8 girls (including Cathy). If 3 students are chosen at random to be studyhall monitors, what is the probability that Doug is selected but Cathy is not?
The random variable X is the number of girls of four children born to a couple...
The random variable X is the number of girls of four children born to a couple that is equally likely to have either a boy or a girl. Its probability distribution is as follows Q24 (a) µ = E(X) = (Round your answer to one decimal place) (b) σ(X) = (Round your answer to one decimal place) c) Among all families with four children, what is the average number of boys? (Round your answer to one decimal place)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT