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Lerok [7]
2 years ago
5

A game of chance involves rolling an unevenly balanced 4-sided die. The probability that a roll comes up 1 is 0.22, the probabil

ity that a roll comes up 1 or 2 is 0.42, and the probability that a roll comes up 2 or 3 is 0.54 . If you win the amount that appears on the die, what is your expected winnings? (Note that the die has 4 sides.)
Mathematics
1 answer:
GuDViN [60]2 years ago
8 0

Answer:

Expected Winnings = 2.6

Step-by-step explanation:

Since the probability of rolling a 1 is 0.22 and the probability of rolling either a 1 or a 2 is 0.42, the probability of rolling only a 2 can be determined as:

P_{1,2} = P_{1}+P_{2}\\P_{2} = 0.42 - 0.22 = 0.20

The same logic can be applied to find the probability of rolling a 3

P_{2,3} = P_{2}+P_{3}\\P_{3} = 0.54 - 0.20 = 0.34

The sum of all probabilities must equal 1.00, so the probability of rolling a 4 is:

P_{4} =1- P_{1}+P_{2}+P_{3} = 1-0.22+0.20+0.34\\P_{4}=0.24

The expected winnings (EW) is found by adding the product of each value by its likelihood:

EW=1*P_{1}+2*P_{2}+ 3*P_{3}+ 4*P_{4} \\EW=1*0.22+2*0.20+ 3*0.34+ 4*0.24\\EW=2.6

Expected Winnings = 2.6

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6. The dimensions of a living room are 18 ft. by 15 ft. by 8ft. If air weighs 0.08 lb. per cubic foot, the weight of the air in
user100 [1]

The weight of the air in the room is 172.8 lb if the dimensions of a living room are 18 ft. by 15 ft. by 8ft.

<h3>What is a rectangular prism?</h3>

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape. It is also called a cuboid.

It is given that:

The dimensions of a living room are 18 ft. by 15 ft. by 8ft.

The volume of the living room = volume of the cuboid:

V = length×width×height

V = 18×15×8

V = 2160 cubic ft

The weight of the air = 0.08 lb. per cubic foot

The weight of the air in the room = 0.08×2160

The weight of the air in the room = 172.8 lb

Thus, the weight of the air in the room is 172.8 lb if the dimensions of a living room are 18 ft. by 15 ft. by 8ft.

Learn more about the rectangular prism here:

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7 0
1 year ago
Please help me I’m so stressed
djverab [1.8K]

This is just like the other problem. The coefficient infront of the b which is "2" is your constant of proportionality. It makes the relationship between the number of bulbs and flowers signaling that for every flower there has to be 2 bulbs.

4 0
3 years ago
Please help me. Thank you!!​
Sliva [168]

Answer:

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Step-by-step explanation:

7 0
2 years ago
What is this expression in simplified form 5/2 times 9/6? A.90 B.90/3 C.45/2 D. 45/3
alekssr [168]

5√2 · 9√6

Simplify.

5 × 9 √ 2 x 6 ⇒ Multiply 2 × 6.

5 × 9 √12

Simplify √12 to 2√3.

5 × 9 × 2√3 ⇔ Multiply

90√3

Therefore, the <u>correct alternative</u> is <u>option "B".</u>

8 0
1 year ago
Sammy counts the number of people in one section of the school auditorium. He counts 18 female students, 16 male students, and 6
Rzqust [24]

Correct Question:

He counts 18 female students, 16 male students, and 6 teachers. There are

720 people in the auditorium. Consider the probability of selecting one person

at random from the auditorium.

Which of these statements are true?

Choose all that apply.

A:  The probability of selecting a teacher is 6%.

B : The probability of selecting a student is 85%.

C : The probability of selecting a male student is 32%.

D : The probability of selecting a female student is 45%.

Step-by-step explanation:

Option B  and D are correct because

The total number of people in one cross section = 18 + 16 + 6 = 40.

A = The probability of selecting a teacher is = (6/40)x100 = 15 % not equal to 6 %

B = The probability of selecting a male student is = (34/40)x100 = 85%

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D : The probability of selecting a female student is = (18/40)x100= 45%

3 0
2 years ago
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