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Maru [420]
3 years ago
10

When Alice spends the day with the babysitter, there is a 0.6 probability that she turns on the TV and watches a show. Her littl

e sister Betty cannot turn the TV on by herself. But once the TV is on, Betty watches with probability 0.8. Tomorrow the girls spend the day with the babysitter. (a) What is the probability that both Alice and Betty watch TV tomorrow? (b) What is the probability that Betty watches TV tomorrow? (c) What is the probability that only Alice watches TV tomorrow? Hint: De ne events precisely and use the product rule and the law of total probability.
Mathematics
1 answer:
lara [203]3 years ago
5 0

Answer:

A. P("Both Alice and Betty watch TV") = 12/25

B. P("Betty watches TV") = 12/25

C. P("Only Alice watches TV") = 3/25

Step-by-step explanation:

A. Because what we are told, Betty need that Alice turn on the TV, so, we first need the probability that she watches TV:

P(Alice)=3/5 (0.6)

And we know that:

P(Betty)=4/5 (0.8)

If we want the probability of both things happening at the same time (If you use a tree diagram, those events will be in the same branch), we proceed multiply them:

P("Both Alice and Betty watch TV") = 3/5 * 4/5 = 12/25

And this is the answer

B. Considering that Betty needs Alice to turn on the TV, the probability of Betty watching TV is the same as if she is with Alice.

P("Betty watches TV") = P("Both Alice and Betty watch TV") = 12/25

C. We use the same process as part A, but with a little difference. We now multiply for the probability that Betty does not watch TV (Because they still be in the same branch).

P("Betty does not watch TV") = 1 - P("Betty")

P("Betty does not watch TV") = 1 - 4/5

P("Betty does not watch TV") = 1/5

And the answer for part C is:

P("Alice watches TV without Betty") = 3/5 * 1/5 = 3/25

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

First Question: Equilateral triangles all have the same interior angles. 60 degrees. Size does not make the angles bigger. It makes the sides bigger.

Second Question: No the size does not influence the size of the interior angle.

Third Question: That's true for all polygons. Size is not affect the interior angle size.

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  102

Step-by-step explanation:

The total of ratio units is ...

  6 + 3 + 8 = 17

The difference between the Charlie's ratio units and Adrian's ratio units is ...

  8 - 6 = 2

That is, the total number of ratio units is 17/2 = 8.5 times that difference.

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3 years ago
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Step-by-step explanation:

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3 years ago
Please someone help me with this word problem for my math class T.T
olga55 [171]

Answer:

<u>Perimeter</u>:

= 58 m (approximate)

= 58.2066 or 58.21 m (exact)

<u>Area:</u>

= 208 m² (approximate)

= 210.0006 or 210 m² (exact)

Step-by-step explanation:

Given the following dimensions of a rectangle:

length (L) = \sqrt{252} meters

width (W) = \sqrt{175} meters

The formula for solving the perimeter of a rectangle is:

P  = 2(L + W) or 2L + 2W

The formula for solving the area of a rectangle is:

A = L × W

<h2>Approximate Forms:</h2>

In order to determine the approximate perimeter, we must determine the perfect square that is close to the given dimensions.  

13² = 169

14² = 196

15² = 225

16² = 256

Among the perfect squares provided, 16² = 256 is close to 252 (inside the given radical for the length), and 13² = 169 (inside the given radical for the width).  We can use these values to approximate the perimeter and the area of the rectangle.

P  = 2(L + W)

P = 2(13 + 16)

P = 58 m (approximate)

A = L × W

A = 13 × 16

A = 208 m² (approximate)

<h2>Exact Forms:</h2>

L = \sqrt{252} meters = 15.8745 meters

W = \sqrt{175} meters = 13.2288 meters

P  = 2(L + W)

P = 2(15.8745 + 13.2288)

P = 2(29.1033)

P = 58.2066 or 58.21 m

A = L × W

A = 15.8745 × 13.2288

A = 210.0006 or 210 m²

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2 years ago
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