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BigorU [14]
3 years ago
8

In the casino game of roulette, a gambler can bet on which of 38 numbers the ball will land when the roulette wheel is spun. On

a $2 bet, a gambler gains $70 (so a net profit of $68) if he or she chooses the winning number, but loses the $2 otherwise. The probability of choosing the winning number is 1/38 and the probability of not choosing the winning number is 37/38. Let X denote the net gain from a roulette spin. What is the expected winnings for one spin?
Mathematics
1 answer:
ollegr [7]3 years ago
4 0

Answer:

Expected winnings for one spin = 0.1

Step-by-step explanation:

Expected Value = Sum of [(Probability of X)(Value of X)]

E(X) = Σ [P(X).X]

Two Events : X = +68 , P(X) = 1/38 and X = -2 , P(X) = 37/38

E(X) = [(68) (1/38)] + [(-2)(37/38)]

[(68)(0.03)] + [(-2)(0.97)]

= 2.04 - 1.94

= 0.1

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Which of the following is a trinomial?
Masja [62]
Although you didn't provide any answer choices:

A trinomial is an expression with exactly three terms that can't be combined an example would be this

x^2 - 3x + 1

None of those terms can be combined

x^2 + 3 - 4 has three terms but it isn't considered a trinomial because you can simplify it to x^2 - 1 which is known as a binomial because it has 2 terms in it's simplified form.

hope this helps C:
5 0
3 years ago
Read 2 more answers
We are throwing darts on a disk-shaped board of radius 5. We assume that the proposition of the dart is a uniformly chosen point
Vlad1618 [11]

Answer:

the probability that we hit the bullseye at least 100 times is 0.0113

Step-by-step explanation:

Given the data in the question;

Binomial distribution

We find the probability of hitting the dart on the disk

⇒ Area of small disk / Area of bigger disk

⇒ πR₁² / πR₂²

given that; disk-shaped board of radius R² = 5, disk-shaped bullseye with radius R₁ = 1

so we substitute

⇒ π(1)² / π(5)² = π/π25 = 1/25 = 0.04

Since we have to hit the disk 2000 times, we represent the number of times the smaller disk ( BULLSEYE ) will be hit by X.

so

X ~ Bin( 2000, 0.04 )

n = 2000

p = 0.04

np = 2000 × 0.04 = 80

Using central limit theorem;

X ~ N( np, np( 1 - p ) )

we substitute

X ~ N( 80, 80( 1 - 0.04 ) )

X ~ N( 80, 80( 0.96 ) )

X ~ N( 80, 76.8 )

So, the probability that we hit the bullseye at least 100 times, P( X ≥ 100 ) will be;

we covert to standard normal variable

⇒ P( X ≥  \frac{100-80}{\sqrt{76.8} } )

⇒ P( X ≥ 2.28217 )

From standard normal distribution table

P( X ≥ 2.28217 ) = 0.0113

Therefore, the probability that we hit the bullseye at least 100 times is 0.0113

3 0
3 years ago
Find the measure of angle x in the figure below: A.) 35° B.) 48° C.) 69° D.) 78°
prisoha [69]

Answer:

x = 48

Step-by-step explanation:

First find y

52+y+59 = 180 since they from a straight line

y = 180-59-52

y = 69

Then we know the angles of a triangle add to 180

x+y+63 = 180

x+69+63 = 180

x = 180-69-63

x =48

3 0
3 years ago
Read 2 more answers
Choose the right symbol: <,>,= a)3- ... -8 b) -4 ... 10 c) 0 ... -1 d) +3 ... 0 e) -5 ... -|-5|
Gre4nikov [31]

Answer:

-3 > -8

-4 < 10

0 > -1

-5 = -5

Step-by-step explanation:

one is bigger than the other hopes this helps

7 0
3 years ago
It takes Andrew 720 seconds to take a shower. He spends an additional 420 seconds eating breakfast.
krok68 [10]

Answer:

Andrew takes for a shower = 720 sec

1 min =60sec

720sec=12min

Andrew takes additional min for breakfast =420 sec

420 sec = 7min

time andrew take for both = 12+7

=19 min

Step-by-step explanation:

4 0
3 years ago
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