Thursday

July 24, 2014

July 24, 2014

Posted by **Anne** on Thursday, March 22, 2012 at 1:15am.

- Probability -
**drwls**, Thursday, March 22, 2012 at 3:08amThe 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.

**Related Questions**

math - suppose that you roll a pair of 8-sided dice total of 51 times. what is ...

statistic - Roll two 6-sided dice and examine their sum. a) How long will it ...

Math - PLEASE - I roll twelve 4-sided dice. What is the probability that I roll ...

Math - Statistics - I roll 12 4-sided dice. What is the probability that I roll ...

Probability plz help - Roszena rolls two standard six-sided dice. If the sum of ...

probability - a student rolls three standard six-sided dice. what is the ...

statistics - The below table shows the probabilities generated by rolling one ...

Probability - You roll two dice. What is the probability that the sum of the ...

biology - One rule of probability can be expressed as the following: The ...

biology - One rule of probability can be expressed as the following: The ...