Question

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?

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

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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

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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