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gregori [183]
3 years ago
5

A number cube with faces labeled 1 through 6 is rolled 200 times. About how many times would you expect to roll an even number?

Mathematics
1 answer:
Sergio039 [100]3 years ago
7 0

Answer:

The theoretical probability is smaller than the relative frequency

Step-by-step explanation:

6-sided cube rolled 200 times

Probability of an even number is 1/2= 0.5

200*1/2= 100- theoretical probability

Experimental frequency= 115

Relative frequency= 115/200= 0.575

0.575 > 0.5

The theoretical probability is smaller than the relative frequency

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ioda
The answer is 8
Here's why:
{ ( \frac{( {6}^{7}) \times ( {3}^{3})  }{(  {6}^{6}) \times ( {3}^{4}  ) } )}^{3}  =   \\ ( \frac{6}{3} ) ^{3}  =  \\ \frac{216}{27}  = 8
The exponents are subtracted one from another when divided.
\frac{ a ^{b} }{ {a}^{c} } =  {a}^{b - c}
We can look at the problem this way:
( \frac{6^{7} }{6 ^{6} }  \times  \frac{3^{3} }{ {3}^{4} } ) = (6^{7 - 6}  \times  {3}^{3 - 4} ) =  \\ ({6}^{1}  \times  {3}^{ - 1} )
Since we have the power of -1 on the 3, we apply this rule:
{a}^{ - b}  =  \frac{1}{ {a}^{b} }
Also this rule because we have the power of 1 on the 6:
{a}^{1}  = a
Then we get this:
(6 \times  \frac{1}{3} )^{3}  = ( \frac{6}{3} )^{3}
We apply the rule:
( \frac{a}{b}) ^{c}   =  \frac{ {a}^{c} }{ {b}^{c} }
We get this:
\frac{{6}^{3} }{ {3}^{3} } =  \frac{216}{27}  = 8
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