1. ## Basic Probability Questions.

1.) In the first half of the year, you are asked to read 10 of the short stories. Your teacher provides you with 25 short stories. How many different ways are there to choose your 10 stories?

2.) In the second half of the year, your teacher has 33 short stories to choose from. You are asked to read 12 stories this time. How many different ways are there to choose the 12 stories to read?

3.)The probability that you will make the hockey team is 2/3. The probability that you will make the swimming team is 3/4. If the probability that you make both teams is 1/2, what is the probability that you at least make one of teams? that you make neither of the team?

4.) In order to choose a mascot for a new school, 2755 students were surveyed: 896 chose a falcon, 937 chose a ran, and 842 chose a panther. The remaining students did not vote. A student is chosen at random.

- What is the probability that the student's choice was a panther?

- Was not a ram?

- Was either a falcon or a ram?

5.)

35 students in an Algebra 2 class took a test: 9 received A's, 18 Received B's, and 8 Received C's. Find the prob of a given even.

- IF a student from the class is chosen at random, what is the probbaility that the student did not receive a C?

- If the teacher randomly chooses 3 test papers, what is the probability that the teacher chose tests with grades A, B, and C in that order?

for 5, im guessing... add the prob of A and B?

for 4, 842/2755?

1.) 10(25) ---?????

2.) 12(33) -----?

2. For Q 1 & 2 it depends on whether the order of reading is important or not. IE is reading A then B different from reading B then A. From the wording it sounds like order is not important and therefore you are interested in the combination. In that case

(Q1)

$\displaystyle C = \frac{25!}{10!(25-10)!} = 3,268,760$

(Q2)

$\displaystyle C = \frac{33!}{12!(33-12)!} = 354,817,320$

I guess the lesson is a small change in the initial parameters can lead to a big difference in the number of combinations.

(Q3)

These two questions sum to one. So the chance of make at least one team = 1 - the chance of making none.

Chance of making none is

$\displaystyle p_0 = (1-2/3)(1-3/4) = 1/12$
Therfore the chance of making at least one is

$\displaystyle p_1 = 11/12$

Another way of seeing this is to draw a Venn diagram.

(Q4)

This is just a straightforward division of number by population so

$\displaystyle p_{panther} = 842/2755$

$\displaystyle p_{not ram} = 1 - p_{ram} = 1 - 937/2755$

$\displaystyle p_{falcon|ram} = p_{falcon} + p_{ram} = (896 + 937)/2755$

(Q5)

This is similar to Q4.

$\displaystyle P_{not C} = 1 - p_C = 1 - 8/35$

In part two you are after an A, B and C in a specific order, so in contrast to Q1 this is a permutation and not a combination.

$\displaystyle p = 9/35 \times 18/34 \times 8/33 = 216/6545$

3. Originally Posted by NYCKid09
1.) In the first half of the year, you are asked to read 10 of the short stories. Your teacher provides you with 25 short stories. How many different ways are there to choose your 10 stories?

Mr F says: $\displaystyle {\color{red} ^{25}C_{10}}$

2.) In the second half of the year, your teacher has 33 short stories to choose from. You are asked to read 12 stories this time. How many different ways are there to choose the 12 stories to read?

Mr F says: $\displaystyle {\color{red} ^{33}C_{12}}$

3.)The probability that you will make the hockey team is 2/3. The probability that you will make the swimming team is 3/4. If the probability that you make both teams is 1/2, what is the probability that you at least make one of teams? that you make neither of the team?

Mr F says:
$\displaystyle {\color{red} \frac{2}{3} + \frac{3}{4} - \frac{1}{2}}$.

4.) In order to choose a mascot for a new school, 2755 students were surveyed: 896 chose a falcon, 937 chose a ran, and 842 chose a panther. The remaining students did not vote. A student is chosen at random.

- What is the probability that the student's choice was a panther?

- Was not a ram?

- Was either a falcon or a ram?

Mr F says: Draw a Venn diagram.

5.)

35 students in an Algebra 2 class took a test: 9 received A's, 18 Received B's, and 8 Received C's. Find the prob of a given even.

- IF a student from the class is chosen at random, what is the probbaility that the student did not receive a C?

Mr F says: $\displaystyle {\color{red} 1 - \frac{8}{35}}$

- If the teacher randomly chooses 3 test papers, what is the probability that the teacher chose tests with grades A, B, and C in that order?

Mr F says: (9/35)(18/34)(8/33) = ....

for 5, im guessing... add the prob of A and B?

for 4, 842/2755?

1.) 10(25) ---?????

2.) 12(33) -----?

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