two number cubes were rolled 150 times a sum less than four appeared 15 times?

Answer 1

Hi,

Since each cube could come up from a 1 to a 6, there are 6 x 6 or 36 possible combinations. Of those only 1 + 1, 1 + 2, or 2 + 1 are the only 3 of the 36 possibilities that add to a sum less than 4.

3 of 36 means that one twelfth of the 150 rolls should be expected to be less than a total of 4. 1/12 of 150 is about 12.5 times should have been less than 4. That means this occurred slightly more often than you would predict.

However, if you threw another 150 rolls, the total could just as easily be less often than you would predict.

I hope that answers what you wanted. :-)

Answer 2

I will give this a shot. I'm assuming that you are seeking the probability of exactly eighteen appearances. I also assuming the number cubes are dice, with numbers running from 1 to 6 on each one. A die has six sides. For a pair of dice, there are 36 possibilities (6 * 6). There are exactly 6 different ways you can get less than five from those two dice (1 & 1, 1 & 2, 1 & 3, 2 & 2, 2 & 1, 3 & 1). The odds of getting it is 6/36, or 1/6. The odd of getting anything else is 30/36, or 5/6. So, for this particular situation, the probability would be (1/6)^18 * (5/6)^82. I won't bother to actually figure out what that number is. I hope that helps.

Answer 3

So far, so good... but what's the question?

In any case, P(2) = 1/36 and P(3) = 2/36
so the odds of rolling less than 4 is 3/36, or 1/12
so in 150 rolls, you'd expect to get a sum less than four roughly 150 * (1/12) = 12.5 times.

15 is slightly more than you'd expect, but not unreasonably so. For whatever that may be worth.

Answer 4

What is your question?