Mr. Hauseman has 17 students in his class, three of whom are freshmen, and the rest are from other classes. He is going to draw two students randomly to be partners.
He calculates the probability of drawing a freshman and then a junior to be
9
136
. How many juniors must be in the class?
3/17 are freshmen
If there are x juniors, then
P(freshman,junior) = 3/17 * x/16 = 3x/272 = 9/136
so, x=6
Thanks for helping me.
To find out how many juniors must be in the class, we can set up an equation based on the given probability.
Let's assume that there are "x" juniors in the class.
The probability of drawing a freshman on the first draw is:
P(Freshman) = (3/17)
After one freshman has been chosen, there will be "x-1" juniors remaining in the class, out of a total of "17-1=16" students. Therefore, the probability of drawing a junior on the second draw is:
P(Junior) = (x-1)/16
The overall probability of drawing a freshman and then a junior is given as 9/136.
So, we can set up the equation as follows:
P(Freshman) * P(Junior) = 9/136
(3/17) * (x-1)/16 = 9/136
Now, we can solve this equation to find the value of x.
(3/17) * (x-1)/16 = 9/136
Cross-multiplying, we get:
(3/17) * (x-1) = (9/136) * 16
Multiplying both sides by 17 to get rid of the fraction, we have:
3(x-1) = (9/136) * 16 * 17
Simplifying, we get:
3x - 3 = (9/136) * 272
3x - 3 = 18
3x = 18 + 3
3x = 21
x = 21/3
x = 7
Therefore, there must be 7 juniors in the class.
To find the number of juniors in Mr. Hauseman's class, we need to set up an equation based on the given information.
Let's assume that the number of juniors in the class is 'x.'
We know that there are 17 students in total, of which three are freshmen. Therefore, the number of students who are not freshmen is (17 - 3) = 14.
The probability of drawing a freshman and then a junior can be calculated as follows:
Probability = (Number of freshmen / Total number of students) * (Number of juniors / Remaining number of students)
According to the problem, the probability is 9/136. We can set up the equation as follows:
(3/17) * (x/14) = 9/136
To solve for 'x,' we can cross-multiply:
3 * x * 136 = 17 * 14 * 9
408x = 2142
Now, we can solve for 'x' by dividing both sides of the equation by 408:
x = 2142 / 408
Simplifying this, we find:
x ≈ 5.25
Since we are looking for the number of juniors, we cannot have a fraction of a student. Therefore, we round up to the nearest whole number.
Therefore, there must be at least 6 juniors in Mr. Hauseman's class in order for the given probability to be true.