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Suppose you roll a standard six-sided die 186 times. How many more times would you expect to roll an even number than roll a 5 or 6 ?
athen your want them

Suppose you roll a standard six-sided die $186$ times. How many more times would you expect to roll an even number than roll a $5$ or $6$ ? $\newline$ athen your want them

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Full solution

Q. Suppose you roll a standard six-sided die

186

times. How many more times would you expect to roll an even number than roll a

5

or

6

?

\newline

athen your want them

Even Number Probability: There are $3$ even numbers on a six-sided die: $2$ , $4$ , and $6$ . The probability of rolling an even number is $\frac{3}{6}$ or $\frac{1}{2}$ .
Expected Rolls of Even Numbers: To find the expected number of times you'd roll an even number in $186$ rolls, multiply the probability by the number of rolls: $(\frac{1}{2}) \times 186 = 93$ .
$5$ or $6$ Probability: There are $2$ numbers that are either $5$ or $6$ on a six-sided die. The probability of rolling a $5$ or $6$ is $\frac{2}{6}$ or $\frac{1}{3}$ .
Expected Rolls of $5$ or $6$ : To find the expected number of times you'd roll a $5$ or $6$ in $186$ rolls, multiply the probability by the number of rolls: $(\frac{1}{3}) \times 186 = 62$ .

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