# Help with probability problems

• sneaky666
In summary: So after i get the first result, i removed all die that have the number 2 in it's value. And then 9 more die are generated. Then i did the same thing with the number 1, so i removed all die that have the number 1 in it's value. And then 9 more die are generated. so thats 45 combinations. But thats not the total number of combinations because i also removed the number 3 and the number 5. So the total number of combinations is 52.
sneaky666

## Homework Statement

1. Suppose we roll 10 fair 6-sided dice. What is the probability that there are exactly two 2's showing?
2. Suppose we are dealt five cards from a standard 52-card deck. What is the probability that
a) we get all 4 aces and the king of spades
c) we get no pairs (all are different values)
d) a full house (3 of a kind and 2 of a kind)

## Homework Equations

This one is correct:
there are 2 pots
in pot1 there is 5 red balls and 7 blue balls
in pot2 there is 6 red balls and 12 blue balls
3 balls are chosen randomely from each pot
chances of all 6 balls to be same color = P(A)
chances of all 6 balls to be red = P(B)
chances of all 6 balls to be blue = P(C)

P(A) = P(B or C)
=P(B) + P(C) -0
P(B)=|B|/|S| = |B|/(12choose3)(18choose3) =
(5choose3)(7choose0)(6choose3)(12choose0)/(12choose3)(18choose3) = 5/4488
P(C)=|C|/|S| = |C|/(12choose3)(18choose3) =
(5choose0)(7choose3)(6choose0)(12choose3)/(12choose3)(18choose3) = 35/816
P(A) = 5/4488 + 35/816 - 0 = 395/8976

## The Attempt at a Solution

1.
number of outcomes = 6^10 = 60466176
10!/2!8! = 45
so i get
45/60466176

2.
number of outcomes = 52x51x50x49x48 / 5x4x3x2x1 = 2598960
a) Here i have two different methods, i don't know if both are wrong or one is right...
method 1
(4choose1 * 4choose4 ) / 2598960 = 1/649740
method 2
( (13choose1) * (13choose1) * (13choose1) * (13choose1) ) / 2598960 = ~0.066
b)
(13choose5)/2598960 = ~4.95x10^(-4)
c)
( (4choose1)*(4choose1)*(4choose1)*(4choose1)*(4choose1) ) /2598960 = ~3.95x10^(-4)
d)
(4choose3)*(4choose2) /2598960 = 1/108290

Let's look at (1) first. The number of ways to choose 2 of the 10 die to be rolled a 2 is 45, but that's not the total number of configurations in which exactly 2 die show a 2. Why not?

I don't get how to complete it. I am too lost...

Last edited:
anyone?

Tedjn said:
Let's look at (1) first. The number of ways to choose 2 of the 10 die to be rolled a 2 is 45, but that's not the total number of configurations in which exactly 2 die show a 2. Why not?

I don't under stand what i am doing wrong
i did
10x9 / 2x1 = 45
10x9 is because after i get one result there's 9 dice, and divinding it by 2! means i am removing all repeated sequences.

## 1. What is probability and how is it calculated?

Probability is the measure of the likelihood that an event will occur. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

## 2. What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability is based on actual data collected from experiments or observations.

## 3. How do you calculate the probability of independent and dependent events?

The probability of independent events is calculated by multiplying the individual probabilities of each event. The probability of dependent events is calculated by taking into account the impact of one event on the other.

## 4. What is a probability distribution?

A probability distribution is a function that shows the possible outcomes of an event and the probability of each outcome occurring. It is used to determine the likelihood of different outcomes in a random experiment.

## 5. How can I use probability to make predictions?

Probability can be used to make predictions by calculating the likelihood of a certain event occurring. By understanding the probability of different outcomes, we can make informed decisions and predict future outcomes with a certain degree of confidence.

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