A fair die is rolled $180$ times. The expected number of $6$ is

50

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30

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10

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5

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Solution

The correct option is B $30$
When a fair die is rolled once, the probability of getting a six is $\frac{1}{6}$ .
When a fair die is rolled twice, the sample space contains $6^{2} = 36$ outcomes.
The probability of getting a six is $\frac{6}{36} = \frac{1}{6}$
Hence the number of expected 6 when a fair die is rolled n times is
$= n \frac{1}{6}$

$= \frac{180}{6}$
$= 30$

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A fair die is rolled 180 times. The expected number of 6 is

The correct option is B 30When a fair die is rolled once, the probability of getting a six is 16.When a fair die is rolled twice, the sample space contains 62=36 outcomes.The probability of getting a six is 636=16Hence the number of expected 6 when a fair die is rolled n times is =n16=1806=30

A fair die is rolled $180$ times. The expected number of $6$ is