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by gmobley10 » Sat Jun 22, 2013 4:17 pm
Here are two questions that I am completely stuck on. Im not even sure if they would be solved via permutation/combination formulas...
In the second I am so confused because it seems like the first sentence answers the question... PLEASE if you know the formula for either of these can you possibly take the time to show me your process? I am just so stumped as to how to approach these two.

1. The Gallup Poll reported that 52% of Americans used a seat belt the last time they got into a car. If 4 people are selected at random, find the probability that they all used a seat belt the last time they got into a car.

2. At a large university, the probability that a student takes calculus and on the dean's list is 0.042. The probability that a student is on the dean's list is 0.21. Find the probability that the student is taking calculus, given that he or she is on the dean's list.
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by vivekchandrams » Sat Jun 22, 2013 9:46 pm
Hi gmobley10,

I guess this might help you.

1. The question says 52% used a seat belt. And 4 people are selected at random.

Let's solve a simpler one. There are 15 blue balls and 10 red balls in a bag. What's the probability of getting all red when 4 balls are drawn at random.

The solution for this is:

10 C 4 / 25 C 4

Now, coming to our problem, we can't make a decision on the total number of people in the sample. That 52% could be from a sample of 100, 200 or even 1000.

In the first case, the procedure would be
52 C 4 / 100 C 4

In the second case, the procedure would be
104 C 4 / 200 C 4.

Solving the two would NOT result in the same answer.

Hence, according to me, some more data is necessary to solve this question.


2. The question stem says - the probability that a student takes calculus as well as in the dean's list is 0.042. Next, the probability that a student is on the dean's list is 0.21.
The question requires you to find the probability of finding a calculus student on the dean's list. So now your entire set is limited to the dean's list. Not the entire school.

This can be obtained by the following:

Let the probability of the students choosing calculus on the dean's list be x .

0.042 is obtained by this process - it is the product of the probability of the student to be present on the dean's list and the probability of the student to choose calculus.

Hence, 0.042 = x * 0.21

x = 0.2


Pls hit ' thank' if you find my post useful.
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