# Thread: Probability Questions

1. ## Probability Questions

I always have disliked probablility...

So... I need some help.. If you will please much appreciated..

How many different signals can be made using four flags of different colors on a vertical flagpole if exactly three flags are used for each signal?

How many 5 letter code words are possible in the word SKATE

Thanks )

2. Originally Posted by skyslimit
I always have disliked probablility...

So... I need some help.. If you will please much appreciated..

How many different signals can be made using four flags of different colors on a vertical flagpole if exactly three flags are used for each signal?

How many 5 letter code words are possible in the word SKATE

Thanks )
Q1. $\displaystyle ^4 P_3 = (4)(3)(2) = 24$ (since the order is important).

Q2. 5! = ....

3. OK...

Also, if you will please check my answer on this one:

If a box of soda contains 36 bottles, 8 are white, 5 are tan 6 are pink 1 is purple, 2 are yellow, 4 is orange, 10 are green

Select 9 bottles randomly, probability that 3 are white

My answer: 8 c 3 / 36 c 9 ? This is right or is there more to it...

Harder problem..

Probability that 3 are white, two are tan, one is pink, one is yellow, and and two are green

4. Originally Posted by skyslimit
OK...

Also, if you will please check my answer on this one:

If a box of soda contains 36 bottles, 8 are white, 5 are tan 6 are pink 1 is purple, 2 are yellow, 4 is orange, 10 are green

Select 9 bottles randomly, probability that 3 are white

My answer: 8 c 3 / 36 c 9 ? This is right or is there more to it... Mr F says: There's more to it - see below.

Harder problem..

Probability that 3 are white, two are tan, one is pink, one is yellow, and and two are green Mr F says: Please post the harder problem exctly as it's written.
$\displaystyle \frac{^8C_3 \cdot {\color{red}^{28}C_6}}{^{36}C_9}$

5. Harder problem
If you select 9 bottles, without replacement, what it is probability that 3 will be white, 2 will be tan, 1 is pink, one is yellow, and two are green?

And one last one after that... seems simple but quickly turns complicated,

How many sundaes?

Ice Cream Flavors

Chocolate
Strawberry
Mint

Toppings

Nut
Caramel
Gummy Bears
Oeros
Fudge
Butterscotch

How many sundaes are possible when choosing 1 sundae and one topping?

Help much appreciated... Again not my favorite subject to deal with in math

6. ## Probability

Hello skyslimit
Originally Posted by skyslimit
Harder problem
If you select 9 bottles, without replacement, what it is probability that 3 will be white, 2 will be tan, 1 is pink, one is yellow, and two are green?
The total number of ways of selecting 9 from 36 is $\displaystyle \binom{36}{9}$.

You then have to choose:

• 3 white from 8. This can be done in $\displaystyle \binom83$ ways.
• 2 tan from 5. This can be done in $\displaystyle \binom52$ ways.
• 1 pink from 6. This can be done in $\displaystyle \binom??$ ways

• 1 yellow from 2 ...?

• 2 green from 10 ...?

When you have filled in the gaps in the last three, there are then two things that you need to do to complete the calculation:

1. Multiply all 5 of these answers together to find the total number of ways of choosing all 5 colours.
2. Divide this answer by $\displaystyle \binom{36}{9}$ to find the probability that one of these selections occurs.

And one last one after that... seems simple but quickly turns complicated,

How many sundaes?

Ice Cream Flavors

Chocolate
Strawberry
Mint

Toppings

Nut
Caramel
Gummy Bears
Oeros
Fudge
Butterscotch

How many sundaes are possible when choosing 1 sundae and one topping?
Use the same principle here. It's called the r-s principle, and it is:

• If a task A can be carried out in $\displaystyle r$ ways, and an independent task B can be carried out in $\displaystyle s$ ways, then the number of ways in which both tasks can be carried out is $\displaystyle r \times s$.

So:

• How many ways are there of choosing an ice-cream flavour?
• How many ways are there of choosing a topping?
• Are these tasks independent of each other? (In other words, can any one of the ice-creams be combined with any of the toppings?) Answer: yes!

Then use the r-s principle and multiply your two numbers together to find the total number of sundaes.

If you want us to check your answers, post them here.

7. Originally Posted by mr fantastic
$\displaystyle \frac{^8C_3 \cdot {\color{red}^{28}C_6}}{^{36}C_9}$
For this one, my question, the 28c6 is derived exactly from where? I have it as being being (28): white subtracted from total of 36, and 6, the leftover of selected bottles. Is this right?

Also, for the harder one with multiple functions, do we not need to include what we have included previously?

And for the sundae problem I worded it wrong. it is supposed to say, 1 flavor 3 toppings. Is 3 (choices) * 6 * 6 * 6 (toppings) right??

8. ## Probability

Hello skyslimit
Originally Posted by skyslimit
For this one, my question, the 28c6 is derived exactly from where? I have it as being being (28): white subtracted from total of 36, and 6, the leftover of selected bottles. Is this right?
Correct!
Also, for the harder one with multiple functions, do we not need to include what we have included previously?
No. This is a separate question. So you begin again in the way that I explained.

And for the sundae problem I worded it wrong. it is supposed to say, 1 flavor 3 toppings. Is 3 (choices) * 6 * 6 * 6 (toppings) right??
No. First, there are 4 choices of flavour, not 3. Then, it depends upon whether the 3 toppings must all be different. If you're allowed to choose the same topping more than once, then the answer is 4 x 6 x 6 x 6. But if they must all be different, then it's $\displaystyle 4 \times \binom{6}{3}$.

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# how many signals can be given by six flags of different colors when any number of them are used?

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