Use the formula the probability nto calculate the expected number throws
Solved Step by Step With Explanation- Dice Expectations: Avg. Numbers & Throws
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Solved Step by Step With Explanation- Dice Expectations: Avg. Numbers & Throws
On the second throw, you want to get a different number than the one you got on the first throw. There are 5 remaining numbers out of the 6 total, so the probability of getting a unique number on the second throw is 5/6.
On the third throw, you want to get a different number than the ones you got on the first two throws. There are 4 remaining numbers out of the 6 total, so the probability of getting a unique number on the third throw is 4/6.
E = 1 + 2(1) + 3(5/6) + 4(4/6) + ... + 10(probability of getting a different number on the 10th throw)
Calculating this expression will give you the expected number of different numbers, which is approximately 5.48.
Here, "n" is the number of throws. The probability that you haven't rolled all 6 numbers decreases with each additional throw.
Now, to find the expected number of throws before you've rolled all 6 numbers at least once, we use the formula:
So, on average, it takes about 6.86 throws to roll all 6 numbers at least once when rolling a six-sided dice.
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