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3 years ago

You roll a six-sided die twice. What is the probability of rolling a 3 and then a 5? A) 1 3 B) 1 6 C) 1 12 D) 1 36

Mathematics

2 answers:

Dominik [7]3 years ago

7 0

Answer: 1/36

Step-by-step explanation: In this problem, we're given that a number cube is rolled twice and we're asked to find the probability of rolling a 3 and a 5.

It's important to understand that the 2 rolls of the number cube are independent events because the result of 1 roll does not affect the result of the other roll.

To find the probability of two independent events, we first find the probability of each event, then we multiply the probabilities.

So let's first find the probability of rolling a 3 with our first role of the number cube. We can find the probability of an event using the ratio below.

Number of favorable outcomes/total number of outcomes

Since there is only one way to roll a 3 and there are six possible outcomes 1, 2, 3, 4, 5, and 6, the probability of rolling a 3 is 1/6.

Next, we find the probability of rolling a 5 with our second role of the number cube which would also be 1/6 because each side is as likely to come up as another number.

Now, to find the probability of rolling a 3 and a 5, we simply multiply the probabilities. Multiplying across the numerators, 1 · 1 is 1 and multiplying across the denominators, 6 · 6 is 36.

This means the probability of rolling a 3 and then a 5 is 1/36.

Molodets [167]3 years ago

4 0

Answer:

D) 1/36

Step-by-step explanation:

You are trying to roll a 3 the first time, and then a 5 the second time. This means that order matters.

It is given to you, that you are rolling a standard die (6-sides). The dice is ordered in the following: 1, 2, 3, 4, 5, 6

The first time, you are rolling for a 3. Note that there is only one 3 in the sequence, so your chance of rolling a 3 is 1 out of 6: 1/6.

The second time, you are rolling for a 5. Note that there is only one 5 in the sequence, so your chance of rolling a 5 is 1 out of 6: 1/6.

Next, multiply the two fractions together to find the probability of rolling a 3 and then a 5:

1/6 x 1/6 = (1 x 1)/(6 x 6) = 1/36

D) 1/36 is your answer.

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Aleksandr [31]

Answer:

$y=3.529 x +37.91$

We can predict the sales representative travelled 8 miles replacing x =8 and we got:

$y(8) = 3.529*8 + 37.91= 66.142$

And we can predict the sales representative travelled 11 miles replacing x =11 and we got:

$y(11) = 3.529*11 + 37.91= 76.729$

Step-by-step explanation:

For this case we have the following data:

Miles Traveled x: 2,3,10,7,8,15,3,1,11

Sales y :31,33,78,62,65,61,48,55,120

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i =60$

$\sum_{i=1}^n y_i =553$

$\sum_{i=1}^n x^2_i =582$

$\sum_{i=1}^n y^2_i =39653$

$\sum_{i=1}^n x_i y_i =4329$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=582-\frac{60^2}{9}=182$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=4329-\frac{60*553}{9}=642.33$

And the slope would be:

$m=\frac{642.33}{182}=3.529$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{60}{9}=6.67$

$\bar y= \frac{\sum y_i}{n}=\frac{553}{9}=61.44$

And we can find the intercept using this:

$b=\bar y -m \bar x=61.44-(3.529*6.67)=37.91$

So the line would be given by:

$y=3.529 x +37.91$

We can predict the sales representative travelled 8 miles replacing x =8 and we got:

$y(8) = 3.529*8 + 37.91= 66.142$

And we can predict the sales representative travelled 11 miles replacing x =11 and we got:

$y(11) = 3.529*11 + 37.91= 76.729$

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