10 is the expected value of the number of times a 2, 3, or 4 will be rolled if a standard six-sided die is rolled 20 times.
Here given that 2, 3 and 4 which 3 faces out of all 6 faces of a dice, so we have information that
No. of faces = 3
faces in dice = 6
Probability = 3/6 or 1/2
No. of times 2, 3, or 4 will be rolled if a standard six-sided die is rolled
⇒ if the probability 1 roll = 1/2
Then
⇒ 20 times roll = 20 × 1/2
= 10
In probability and statistics, concerns involving rolling the dice are particularly common. If you roll a six-sided die, you might be asked what the likelihood is of rolling a five and a seven, a double twelve, or a double-six.
While you *could* theoretically utilize a formula or two (such as a combinations formula), understanding each number that is part of the formula is truly necessary, and that's not always easy.
Writing out a sample space is by far the simplest (visual) way to answer these kinds of questions, which involve determining the likelihood of rolling a particular combination or group of numbers.
Learn more about probability
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