Answer:
[tex]P( eleventh\: \: |\: \: FT)= 0.2453 \\\\P( eleventh\: \: |\: \: FT)= 24.53\% \\\\[/tex]
Step-by-step explanation:
We are given a joint probability table.
There are four different graders in a school
1. Grade Ninth
2. Grade Tenth
3. Grade Eleventh
4. Grade Twelfth
Field trip refers to the students who will attending the amusement park field trip.
No field trip refers to the students who will not be attending the amusement park field trip.
We want to find out the probability that the selected student is an eleventh grader given that the student is going on a field trip.
[tex]P( eleventh\: \: |\: \: FT)= \frac{P( eleventh\: \: and \: \: FT)}{P(FT)}[/tex]
Where P(eleventh and FT) is the probability of students who are in eleventh grade and will be going to field trip
[tex]P(eleventh\: and \: FT) = \frac{13}{92} \\\\P(eleventh \: and \: FT) = 0.1413[/tex]
Where P(FT) is the probability of students who will be going to field trip
[tex]P(FT) = \frac{12}{92} + \frac{9}{92} + \frac{13}{92} + \frac{19}{92}\\\\P(FT) = 0.1304 + 0.0978 + 0.1413 + 0.2065\\\\P(FT) = 0.576 \\\\[/tex]
So the required probability is
[tex]P( eleventh\: \: |\: \: FT)= \frac{P( eleventh\: \: and \: \: FT)}{P(FT)} \\\\P( eleventh\: \: |\: \: FT)= \frac{0.1413}{0.576} \\\\P( eleventh\: \: |\: \: FT)= 0.2453 \\\\P( eleventh\: \: |\: \: FT)= 24.53\% \\\\[/tex]
