Homework is stumping me. Just need help with these 8.

1. Based on his skill in basketball, it was computed that when Joe threw a free throw, the odds in favor of his making it were 4 to 28 find the probability that when Joe shot a free throw he made it. Out of every 100 free throws he attempted on the average how many did he miss.

2. From 9 names on a ballot, a committee of 5 will be elected to attend a political national convention. How many committees are possible.

3. You are dealt one card from a 52- card deck. Find the probability that you are dealt a numbered card or a spade.

4.A set of data items is normally distributed with a mean of 500. Find the data item in this distribution that corresponds to the given z-score.

z=1.5 if the standard deviation is 50

5. A teacher and 12 students are to be seated along a bench in the bleachers. In how many ways can this be done if the teacher must be seated in the middle and the one difficult student in the class must sit to the teachers immediate left?

6. An ice chest contains 4 cans of apple juice, 3 cans of grape juice, 9 cans of orange juice and 2 cans of pineapple juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting no grape juice.

7. In a contest in which 10 contestants are entered, in how many ways can 4 distinct prizes be awarded.

8.You are dealt 6 cards from a shuffled deck of 52. find the probability of getting 3 jacks and 3 aces.

Thanks for reading. any help is appreciated.

Re: Homework is stumping me. Just need help with these 8.

Hello, juan62488!

Problem #2, 6 and 7 are very basic problems.

If you can't do those, no wonder you're having difficulty.

I'm certain that these 8 problems is your entire assignment.

I can't imagine any problem that you *could* solve.

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2. From 9 names on a ballot, a committee of 5 will be elected to attend a political national convention.

How many committees are possible?

This is a Combinations problem.

Choosing 5 objects from 9, there are: .$\displaystyle _9C_5 \:=\:{9\choose5} \:=\:\frac{9!}{5!\,4!} \:=\: 126 $ ways.

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5. A teacher and 12 students are to be seated along a bench in the bleachers.

In how many ways can this be done if the teacher must be seated in the middle

and the one difficult student in the class must sit to the teachers immediate left?

There are 13 people to arrange in a row.

Duct-tape the teacher and the difficult student together: .$\displaystyle \boxed{TS}$

Now we have 12 "people" to arrange:

. . [TS] and the 11 other students.

Consider the 12 positions: ._ _ _ _ _ _ _ _ _ _ _ _

Since the teacher must be "in the middle",

. . [TS] cannot occupy the first seat; it has 11 choices of seats.

Then the other 11 students can be seated in $\displaystyle 11!$ ways.

Therefore, there are: $\displaystyle 11\cdot 11! \,=\,439,\!084,\!800$ ways.

Quote:

8.You are dealt 6 cards from a shuffled deck of 52.

Find the probability of getting 3 Jacks and 3 Aces.

There are: .$\displaystyle _{52}C_6 \:=\:{52\choose6} \:=\:\frac{52!}{6!\,46!} \:=\:20,\!358,\!520 $ possible outcomes.

We want 3 of the 4 available Jacks: .$\displaystyle _4C_3 \,=\,4$ ways.

We want 3 of the 4 available Aces: . $\displaystyle _4C_3 \,=\,4$ ways.

Hence, there are:.$\displaystyle 4\cdot4 \,=\,16$ ways to get 3 Jacks and 3 Aces.

Therefore: .$\displaystyle P(\text{3 Jacks, 3 Aces}) \;=\;\frac{16}{20,\!358,\!520} \;=\;\frac{2}{2,\!544,\!815}$

Re: Homework is stumping me. Just need help with these 8.

Quote:

Originally Posted by

**juan62488** 1. Based on his skill in basketball, it was computed that when Joe threw a free throw, the odds in favor of his making it were 4 to 28 find the probability that when Joe shot a free throw he made it. Out of every 100 free throws he attempted on the average how many did he miss.

3. You are dealt one card from a 52- card deck. Find the probability that you are dealt a numbered card or a spade.

4.A set of data items is normally distributed with a mean of 500. Find the data item in this distribution that corresponds to the given z-score.

z=1.5 if the standard deviation is 50

6. An ice chest contains 4 cans of apple juice, 3 cans of grape juice, 9 cans of orange juice and 2 cans of pineapple juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting no grape juice.

7. In a contest in which 10 contestants are entered, in how many ways can 4 distinct prizes be awarded.

Being that this is for a homework assignment, please show work on these if you want further help.

-Dan