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marishachu [46]
3 years ago
8

A prisoner is trapped in a cell containing three doors. The first door leads to a tunnel that returns him to his cell after two

days’ travel. The second leads to a tunnel that returns him to his cell after four days’ travel. The third door leads to freedom after one day of travel. If it is assumed that the prisoner will always select doors 1, 2, and 3 with respective probabilities 0.3, 0.5, and 0.2, what is the expected number of days until the prisoner reaches freedom?
Mathematics
1 answer:
Greeley [361]3 years ago
4 0

Answer:

The expected number of days until the prisoner reaches freedom is 2.8.

Step-by-step explanation:

Door 1: 0.3 probability of being selected. Leads to his cell after two days' travel.

Door 2: 0.5 probability of being selected. Leads to his cell after four days' travel.

Door 3: 0.2 probability of being selected. Leads to his cell after one day of travel.

What is the expected number of days until the prisoner reaches freedom?

We multiply the probability of each door being used by the time that it leads to the cell. So

E = 0.3*2 + 0.5*4 + 0.2*1 = 2.8

The expected number of days until the prisoner reaches freedom is 2.8.

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Rama09 [41]

Answer:

Fraction: 1 / 20

Decimal: 0.05


Step-by-step explanation:

Fraction Answer:

step 1: convert the percent to a fraction which would be 5 / 100

step 2: find the greatest common factor which is 5

step 3: divide 5 / 5 = 1

step 4: divide 100 / 5 = 20

step 5: write your new simplified fraction


Decimal Answer:

step 1: convert the percent into a decimal which is 0.05

step 2: write your new decimal answer

4 0
3 years ago
Solve the equation on the<br> interval [0, 27r).<br> 4(sin x)2 - 2 = 0
Ket [755]

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Check the picture below.

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2 years ago
Cee-Lo Green decided to paint his entire house purple! The purple paint mixture contains 1/2
Temka [501]

Answer

Find out the how many cups of red and blue paint would you  need .

To prove

As given

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Thus the ratio of the blue paint to the red paint is given by.

\frac{Blue\ paint}{Red\ paint} = \frac{\frac{1}{2}}{\frac{1}{3}}

Thus

\frac{Blue\ paint}{Red\ paint} = \frac{3}{2}

As given

same ratio to make 20 cups of purple paint .

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Thus

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4 0
3 years ago
Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach measured at high tide where 1
Rudiy27

Answer:

Step-by-step explanation:

1. Erosion patterns

(a) Western Beach

In 15 yr, Western Beach erodes from 100 ft to 70 ft.

The rate of erosion is 30 ft/15 yr = 2 ft/yr.

(b) Dunes Beach

In 15 yr, Dunes Beach builds up from 20 ft to 95 ft.

The rate of buildup is 75 ft/15 yr = 5 ft/yr.

Beaches with equal width

The western beach loses 2 feet each year, every 5 years the beach loses 10 feet. Dunes beach gets 5 feet every year, and every 5 years the beach loses 25 feet.

2.From the table, it appears that the beaches will have the same width sometime in year 11 (2006).

wester beach at 11 years it was 78.

dunes beach it was 75.

and these are the most closest value beatween two  beaches

3. even if the rate remains constant we wont be able to have same width . because the width of weatern beach is decreasing and dunes beach is increasing. so the year their width was almost equal was year 11th. they will never have the same width because western beach is going down in width and dunes is going up.

hope it helps.  hope i get brainlist

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Rashid [163]

Answer:

1.slope is 2

2.slope is -3/5

3.slope is 1

4.vertical line slope 0 undefined

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6.horizontal line slope 0 undefined

Step-by-step explanation:

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3 years ago
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