Question

The table displays the number of students in each grade at Richmond High School who will or will not be attending the amusement park field trip.

a student selected at random. what is the probability, as a decimal to the nearest thousandth, that the selected student is as eleventh grader given that the student is going on a feild trip?

P( 11th l FT)= _____ (decimal to the nearest thousandths)

Answer 1

The probability that a student preferred a class trip to the amusement park given they are in 11th grade is; 0.14

What is the probability?

Total number of students is; 12 + 9 + 13 + 19 + 14 + 11 + 8 + 6 = 92

Number of class trip to the amusement park given they are in the 11th grade = 13

Thus, probability that a student preferred a class trip to the amusement park given they are in 11th grade is;

P(11th grade trip to amusement park) = 13/92

P(11th grade trip to amusement park) = 0.14

Answer 2

`P( eleventh\: \: |\: \: FT)= 0.2453 \\\\P( eleventh\: \: |\: \: FT)= 24.53\% \\\\`

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.

`P( eleventh\: \: |\: \: FT)= (P( eleventh\: \: and \: \: FT))/(P(FT))`

Where P(eleventh and FT) is the probability of students who are in eleventh grade and will be going to field trip

`P(eleventh\: and \: FT) = (13)/(92) \\\\P(eleventh \: and \: FT) = 0.1413`

Where P(FT) is the probability of students who will be going to field trip

`P(FT) = (12)/(92) + (9)/(92) + (13)/(92) + (19)/(92)\\\\P(FT) = 0.1304 + 0.0978 + 0.1413 + 0.2065\\\\P(FT) = 0.576 \\\\`

So the required probability is

`P( eleventh\: \: |\: \: FT)= (P( eleventh\: \: and \: \: FT))/(P(FT)) \\\\P( eleventh\: \: |\: \: FT)= (0.1413)/(0.576) \\\\P( eleventh\: \: |\: \: FT)= 0.2453 \\\\P( eleventh\: \: |\: \: FT)= 24.53\% \\\\`