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Michael has never taken a foreign language class, but is doing a story on them for the school newspaper. The school offers French and Spanish. Michael has a list of all 25 kids in the school enrolled in at least one foreign language class. He also knows that 18 kids are in the French class and 21 kids are in the Spanish class. If Michael chooses two kids at random off his list and interviews them, what is the probability that he will be able to write something about both the French and Spanish classes after he is finished with the interviews

Respuesta :

The probability that kids will be able to write something about both the French and Spanish classes after he is finished with the interviews is 91/100.

Given 25 kids has enrolled in atleast one foreign language class. 18 kids are in French class and 21 kids are in Spanish class.

We have to find the probability that kids will be able to write something about both the French and Spanish classes after Michael is finished with the interviews.

Let F is a set showing students knowing French,

S be a set showing students knowing Spanish ,

FS= Showing students both enrolled in one languages.

FS=F+S-(F∪S)

=18+21-25

=14

F-18-14=4

S=21-14

=7

4 outcomes lead to Michael being able to write both the languages are (F,S),(FS,S)(FS,F)(FS,FS)

Required probability is the sum of all the probabilities of (F,)(FS,S)(FS,F)(FS,FS)

P(F,S)=[tex]4C_{1}*7C_{1}/25C_{2}[/tex]

=(4*7)/300

=28/300

P(FS,S)=[tex](14C_{1}*7C_{1} )/25C_{2}[/tex]

=14*7/300

=98/300

P(FS,F)=[tex](14C_{1}*4C_{1} )/25C_{2}[/tex]

=14*4/300

=56/300

P(FS,FS)=[tex]14C_{2}/25C_{2}[/tex]

=91/300

Required probability=28/300+98/300+56/300+91/300

=(28+98+56+91)/300

=273/300

=91/100

Hence the probability that kids will be able to write both the languages is 0.91.

Learn more about probability at https://brainly.com/question/24756209

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