## Monday, May 28, 2007

### Probability Pre-Test

Hello, i am the class scribe for this evening. We started today's class with a pre-test, because tomorrow is our long awaited test on probability. Basically the Pre-test had lasted almost the full class, because many of the students had questions about the questions on the pre-test. So to not get carried away here are the questions and the solutions to the pre-test questions.

question #1: Twelve people including you are members of the choir. The choir director is going to choose three members to attend a workshop. The probability you and two other members will be chosen is:
a. 1/4 b. 3/10 c. 1/12 d. 1/10

The answer is 1/4, because you are going so it is 1 * 11c2, because there are 11 members left and the director needs to pick two of them. It is all over 12c3, because it is over all the possibilities. So once that is calculated it is 1/4.

question #2: Rex is playing a guessing game. The probability he will guess each question correct is 0.3. What is the probability he will guess exactly 5 out of 10 questions correctly?
a. 0.15 b. 0.10 c. 0.29 d. 0.80

The answer is 0.10, because he must get 5 out of 10 questions correct so it is RRRRRWWWWW.
So it is 10!/5!*5!, because there are 5w's and 5r's. Then the 10!/5!*5! is multiplied by (0.3)^5*(0.7)^5 which is the binomial theorem. So once it is all worked out you achieve the answer of 0.10.

question#3: You choose 4 digits from the numbers (0-9), with no repeated digits. To win a prize only two numbers need to match the four selected by the computer.The probability, correct to the nearest one hundredth that you will win a prize.

The answer is 54.76%, because you must take the amount of numbers you are able to match with the computer to win a prize in this case 4c2, 4c3, or 4c4 numbers and divide them over all the possibilities which is 10c4, and add them all up. Once added and reduced it should give you a fraction:23/42, which is 54.76%.

question#4: The serial number of a \$10 bill contains 8 digits. If your \$10 bill contains the digit 7 at least once, you win a prize. What is the probability that your \$10 bill will win?

The answer is you must find the probability of when there are no 7's and then you take the complement. So no 7's is basically 9 out of the possible 10 numbers to the exponent (^) of 8, because there is 8 digits. It gives you an answer of 0.4305, so to get the probability that there is a 7 you must take the complement, so 1 - 0.4305 = 56.95%. which is the answer.

question#5: Jeff takes a lunch to school on two days, and on the other three days he buys it. If he takes lunch he is late for his fourth period class 15% of the time, but if he buys it, he is late 35% of the time.

A) what is the probability that Jeff arrives on time?

The answer is that we take percentages of the two times he arrives and add them together to form the answer. So P(o) = P(to) + P(bo) = (0.4)(0.85) + (0.6)(0.65) = 73% which is the answer.

B) If Jeff was late, what is the probability that he took his lunch to school?

The answer is that you must take the probability he was late and took his lunch to school divided by the time he was late and brought his lunch plus the time he was late and bought his lunch. (0.4)(0.15)/(0.4)(0.15) + (0.6)(0.35) = 2/9 or 22.22% which is the answer.

So he is all of what we had done in class to day, when viewing this scribe post make sure to check the slides if you are confused, because it may help you find the way I had shown the answer. Make sure to study because tommorow is our Probability Test.

Tommorow's scribe is Robert P.