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Sonja [21]
3 years ago
7

A game involves rolling a fair six-sided die. If the number facing upward on the die is a whole number multiple of three, the pl

ayer wins an amount equal to the number on the die times $20. If the number is not a multiple of three, the player gets nothing. What is the expected value of a player's winnings on each roll?
Mathematics
2 answers:
e-lub [12.9K]3 years ago
7 0

Answer:

$30

Step-by-step explanation:

To find the expected value, first we find the outcomes for the sample space.

Rolling a 6-sided die, we have

1, 2, 3, 4, 5, 6

There are 2 values that are whole number multiples of 3:  3 and 6.

There is a 1/6 chance of rolling a 3 and a 1/6 chance of rolling a 6.

There is a 1/6 chance of rolling a 1, 1/6 chance of rolling a 2, 1/6 chance of rolling a 4, and 1/6 chance of rolling a 5.

Next we multiply the value won or lost by each probability.

If the player rolls a 3, they win 3(20) = 60.  Multiplying it by its probability, we have

1/6(60) = 60/6 = 10

If the player rolls a 6, they win 6(20) = 120.  Multiplying it by its probability, we have

1/6(120) = 120/6 = 20.

If the player rolls a 1, 2, 4 or 5, they win nothing.  0 times all of these will be 0.

Lastly, we add together these products:

10+20+0+0+0+0 = 30

ololo11 [35]3 years ago
4 0
I would say about $10 about 1/6th the time
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Estimate the perimeter and area of the shaded figure to the nearest tenth.
Maru [420]

Answer:

Perimeter = 18.7 units

Area = 13.5 units²

Step-by-step explanation:

Perimeter of ADEC = AD + DE + EC + AC

Length of AD = 3 units

By applying Pythagoras theorem in ΔDBE,

DE² = DB² + BE²

DE² = 3² + 3²

DE = √18

DE = 4.24 units

Length of EC = 3 units

By applying Pythagoras theorem in ΔABC,

AC² = AB² + BC²

AC² = 6² + 6²

AC = √72

AC = 8.49 units

Perimeter of ADEC = 3 + 4.24 + 3 + 8.49

                                 = 18.73 units

                                 ≈ 18.7 units

Area of ADEC = Area of ΔABC - Area of ΔBDE

Area of ΔABC = \frac{1}{2}(AB)(BC)

                       = \frac{1}{2}(6)(6)

                       = 18 units²

Area of ΔBDE = \frac{1}{2}(BD)(BE)

                       = \frac{1}{2}(3)(3)

                       = 4.5 units²

Area of ADEC = 18 - 4.5

                        = 13.5 units²

6 0
3 years ago
The manager of a mechanical pencil company determined that 4 out of every
iren2701 [21]

Answer:

10

Step-by-step explanation:

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3 years ago
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Answer:

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Step-by-step explanation:

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4 0
3 years ago
What is d in d • 24= -12
Firdavs [7]

Answer:

The answer is (-1/2)

Step-by-step explanation:

<h3><u>Given</u>;</h3>
  • d • 24 = (-12)
<h3><u>To </u><u>Find</u>;</h3>
  • The value of d

So,

24d = -12

Divide both side by 24 we get,

24d/24 = -12/24

d = -1/2

Thus, The value of d is (-1/2)

3 0
2 years ago
Read 2 more answers
A man is paid $1500 salary. He spends 20% of the salary for his kids education, 35% for food, 15% for miscellaneous and he saves
Alexxandr [17]
<h3>G I V E N : </h3>

A man is paid $1500 salary. He spends 20% of the salary for his kids education, 35% for food, 15% for miscellaneous and he saves the rest. How much money does he save?

<h3>S O L U T I O N : </h3>

Total Income = $ 1500

According to the question,

He spends 20% to his kids education

He spends 35% for food

He spends 15% for miscellaneous

Out of total income he spends 20% on kids education

So, amount spent on kids education = 20% of $1500

Amount = 20/100 × $1500

Amount = $300

Hence, money spent on his kids education is $300

35% is spent on food

Money spent on food = 35% of $1500

Money spent = 35/100 × $1500

Money spent = $525

Hence, money spent on food is $525

15% is spent on miscellaneous

Money spent on miscellaneous = 15% of $1500

Money spent = 15/100 × $1500

Money spent = $225

Hence, money spent on miscellaneous is $225

Now, adding all the three we get

$300 + $525 + $225

$825 + $225

$1050

Total money spent = $1050

Remaining money = $1500 - $1050 = $450

  • <u>Remaining amount left with him is $450</u>
3 0
3 years ago
Read 2 more answers
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