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3 years ago

A number cube has sides labeled 1 to 6. Connie rolls the number cube 12 times She rolls a 5

Mathematics

1 answer:

Otrada [13]3 years ago

7 0

¹/24

Step-by-step explanation:

The number of favorable outcomes (rolling a 5) is 3

The total number of possible outcomes is 12 * 6 = 72

Therefore;

P(5) = 3/72

= 1/24

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Answer:

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Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

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e = 2.71828 is the Euler number

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This means that for 1 week, $\mu = \frac{3}{20} = 0.15$

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Probability of at most one failure, so:

$P(X \leq 1) = P(X = 0) + P(X = 1)$

Then

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-0.15}*0.15^{0}}{(0)!} = 0.8607$

$P(X = 1) = \frac{e^{-0.15}*0.15^{1}}{(1)!} = 0.1291$

Then

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.8607 + 0.1291 = 0.9898$

0.9898 = 98.98% probability that there will not be more than one failure during a particular week.

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