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3 years ago

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In a bucket, there are 5 red marbles, 3 blue marbles, and 2 green marbles. A marble is chosen randomly and then put back into th

e bucket. Then a 2nd marble is chosen. What is the probability that the first marble was red and the second marble was green

1 answer:

nadezda [96]3 years ago

8 0

Answer:

The required probability is $\frac{1}{10}$ .

Step-by-step explanation:

Probability:

The ratio of the favorable outcomes to the all possible outcomes.

Given that, in a bucket, there are 5 marbles red in color, 3 marbles blue in color and 2 marbles green in color.

Total number of marbles are = 5+3+2= 10

The probability that first marble was red

$=\frac{\textrm{Number of red marbles}}{\textrm{Total number of marbles}}$

$=\frac{5}{10}$

$=\frac12$

The probability that second marble was green is

$=\frac{\textrm{Number of green marbles}}{\textrm{Total number of marbles}}$

$=\frac{2}{10}$

$=\frac15$

The required probability is

$=\frac12 \times \frac15$

$=\frac1{10}$

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Answer:

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Step-by-step explanation:

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Let X the random variable that represent the number of chocolate chips in a certain type of cookie. We know that $X \sim Poisson(\lambda)$

The probability mass function for the random variable is given by:

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And f(x)=0 for other case.

For this distribution the expected value is the same parameter $\lambda$

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On this case we are interested on the probability of having at least two chocolate chips, and using the complement rule we have this:

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Using the pmf we can find the individual probabilities like this:

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And now we can solve for $\lambda$

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Applying natural log on both sides we have:

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