AARahman <[EMAIL PROTECTED]> wrote: > I don't know how to solve this statistics problem. I have tried my best to > workout the solutions but failed. I think my IQ is not up to the mark!
It will help if you express everything in formal notation. > Question: > Assume you have applied for two scholarships, a Merit scholarship (M) and an > Athletic scholarship (A). The probabilitythat you receive an Athletic > scholarship is 0.18. The probability of reveiving both scholarship is 0.11. > The probability of getting at least one of the scholaarship is 0.3. Okay, we want to talk about P(A), the probability of getting an athletic scholarship, which we know is 0.18, and P(M), the probability of getting a merit scholarship, which isn't given but which we can solve for. You've also been given P(M & A), the probability of receiving both (the intersection of two events), as 0.11, and P(M or A), the probability of getting at least one (the union of two events), as 0.3. To solve for P(M), you need to look up the rule for computing the probability of the union of two events. You need to keep in mind that the two events are *not* mutually exclusive; if, for example, the probability of rain on Saturday is 50% and the probability of rain on Sunday is 50%, the probability of rain over the weekend is 75%, *not* 100% (assuming the probabilities are independent). Once you have the rule and the known values, some simple algebra should give you P(M). By the way, as you will discover, the events A and M are *not* independent (the questions below wouldn't make any sense if they were, so you can't solve for P(M) by using the rule for the intersection of two independent events. > a. What is the probability of receiving the athletic scholarship given that > you have been awarded the Merit scholarship? This is written as P(A | M) > b. What is the probability of receiving the Merit scholarship given that > you have been awarded the Athletic scholarship? And this is written as P(M | A). Once you have both P(M) and P(A), you can use the rule for conditional probability to solve both of these. You should also discover that there's a simple relation between the two (hint: if you know both P(A) and P(M) as well as one of the conditional probabilities, you can figure out the other one by a simplified version of Bayes' theorem). . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
