# Probability

posted by .

7) Suppose that you roll a pair of standard 6-sided dice a total of 42 times. What is the probability that you will get a sum of 5 at least four times?

• Probability -

The probability of getting 5 on one toss of a pair is 1/9. The most probable number of fives you will get after 42 tosses is 4 or 5.

Add the probabilities of getting 5 four, five, six, seven, eight etc timesout of 42 tosses. By the time you get to 15 times, the probability will be very small and you can quit adding them up.

The probability of rolling 5 four times is (1/9)^4*(8/9)^38*42!/(38!*4!)
= 119,930*1.524*10^-4*1.138*10^-2
= 0.20803

The probability of rolling 5 five times is (1/9)^5*(8/9)^37*42!/(37!*5!)
= 8.507*10^5*1.6935*10^-5*1.2804*10^-2
= 0.18447

I am not going to continue this because it would take half the night, but you get the idea.

There is an easier way to do this that just occurred to me. It will give the same answer. Here it is:
Add the probabilities of getting 5 zero, one, two or three times, and subtract that from 1.

The probability of never getting five is (8/9)^42 = 0.007105
The probability of getting 5 only once is (1/9)*(8/9)^41*42 = 0.037304
The probability of getting 5 twice is
(1/9)^2*(8/9)^40*(42*41*/2) = 0.095591
Now YOU compute the probability of getting 5 three times. Add that to the probabilites above and subtract the sum from one. You should end up with a number around 0.6.

That will be the answer.

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### Math - Statistics

I roll 12 4-sided dice. What is the probability that I roll at least one 2?
2. ### Math - PLEASE

I roll twelve 4-sided dice. What is the probability that I roll at least one 2?
3. ### statistics

The below table shows the probabilities generated by rolling one die 50 times and noting the up face. What is the probability of getting an odd up face?
4. ### math

suppose that you roll a pair of 8-sided dice total of 51 times. what is the probability that you will get a sum of 5 at least 3 times
5. ### math

Maryann rolls a 6-sided dice six times. How many ways can she roll the dice so that the sum of her numbers is 10?
6. ### statistic

Roll two 6-sided dice and examine their sum. a) How long will it take to roll "snake-eyes" (a pair of ones)?
7. ### Probability

You roll two five-sided dice. The sides of each die are numbered from 1 to 5. The dice are “fair" (all sides are equally likely), and the two die rolls are independent. Part (a): Event A is “the total is 10" (i.e., the sum of the …
8. ### dice probability (math)

if a pair of fair dice is rolled, what is the probability that we roll a total of five if we are given that the total is less than nine?
9. ### Math

1. If you flip a fair coin 10 times, what is the probability of a) getting all tails Is it 1/1024?
10. ### math

A pair of 6 sided fair dice are rolled. If one of the dice shows an odd number what is the probability of the sum of the dice being 7 ?

More Similar Questions