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iren [92.7K]
3 years ago
14

You roll a pair of fair dice until you roll “doubles” (i.e., both dice are the same). what is the expected number, e[n], of roll

s?
Mathematics
1 answer:
bonufazy [111]3 years ago
3 0

We need to define our outcomes and events.

 

Finding the probability<span> of each event occurring separately, and then multiplying the probabilities is the step to <span>finding  the probability</span> of two independent events that occur in sequence.

</span>

<span>
To solve this problem, we take note of this:</span>

 

The roll of the two dice are denoted by the pair

(I, j) ∈ S={ (1, 1),(1, 2),..., (6,6) }

Each pair is an outcome. There are 36 pairs and each has probability 1/36. The event “doubles” is { (1, 1),(2, 2)(6, 6) } has probability p= 6/36 = 1/6. If we define ”doubles” as a successful roll, the number of rolls N until we observe doubles is a geometric (p) random variable and has expected value E[N] = 1/p = 6.

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Melissa wants to purchase a digital camera.The listed price of the camera is $195.99.The camera is no sale for 10% off and Melis
lianna [129]

Answer:

The 10% off sale will save Melissa <u>$10.49</u>.

Step-by-step explanation:

Given:

The listed price of the camera is $195.99.

The camera is no sale for 10% off and Melissa has a coupon for 5% off the sales tax is 7%.

Now, to find the money Melissa will save of the 10% off sale.

So, to get the price of camera of the 5% off sale:

(195.99-5\%\ of\ 195.99)

=(195.99-\frac{5}{100}\times 195.99)

=(195.99-9.80)

=186.19

Now, adding the sales tax:

186.19+7\%\ of\ 186.19

=186.19+\frac{7}{100} \times 186.19

=186.19+13.03

=199.22

Thus, the price is $199.22.

Now, to get the price of 10% off sale:

195.99-10\%\ of\ 195.99

=195.99-\frac{10}{100} \times 195.99

=176.39

So, adding sales tax:

176.39+7\%\ of\ 176.39

=176.39+\frac{7}{100} \times 176.39

=188.73

Hence, the price is $188.73.

Now, to get the money 10% off sale will save Melissa:

199.22-188.73

=10.49

Therefore, the 10% off sale will save Melissa $10.49.

7 0
3 years ago
Given (21,7) and (x,<br> 1), find all x such that the distance between these two points is 17.
Dmitriy789 [7]

Answer:

21+/-sqrt(253)=x

So one value for x is 21+sqrt(253)

and another is 21-sqrt(253)

Problem:

Given (21,7) and (x,1), find all x such that the distance between these two points is 17.

Step-by-step explanation:

Change in x is x-21

Change in y is 7-1=6

distance^2=(change in x)^2+(change in y)^2

17^2=(x-21)^2+(6)^2

289=(x-21)^2+36

Subtract 36 on both sides:

289-36=(x-21)^2

253=(x-21)^2

Take square root of both sides:

+/-sqrt(253)=x-21

Add 21 on both sides:

21+/-sqrt(253)=x

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Answer:-5

Step-by-step explanation:

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