Posted by Anne on Thursday, March 22, 2012 at 1:15am.
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.
Related Questions
math - suppose that you roll a pair of 8-sided dice total of 51 times. what is ...
Math - PLEASE - I roll twelve 4-sided dice. What is the probability that I roll ...
math - You roll 2 six-sided dice. Give the probability of rolling the total 2.
biology - One rule of probability can be expressed as the following: The ...
biology - One rule of probability can be expressed as the following: The ...
math - anderson will roll two standard six sided dice once. what is the ...
Stats HELP PLEASE - The game of Yahtzee is played with five fair six-sided dice...
Algebra 2 - What is the probability when you roll 2 dice and you roll a number ...
statistic - roll 2 standard dice and add the numbers. what is the probability of...
statistics - Roll 2 standard dice and add the numbers. whats the probability of ...
For Further Reading
