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A roulette wheel has 38 3838 slots, of which 18 1818 are red, 18 1818 are black, and 2 22 are green. In each round of the game, a ball is tossed in the spinning wheel and lands in a random slot. Suppose we watch 7 77 rounds of this game, and let R RR represent the number of rounds where the ball lands in a red slot. Which of the following would find P ( R = 3 ) P(R=3)P, left parenthesis, R, equals, 3, right parenthesis?

Sagot :

MrRoyal

The value of P(R = 3) is 0.2854

Probability

Probabilities are used to determine the chances of events.

The given parameters are:

  • [tex]n = 38[/tex] --- the number of slots
  • [tex]red = 18[/tex]. --- the number of red slot
  • [tex]black = 18[/tex]. --- the number of black slot
  • [tex]green = 2[/tex]. --- the number of green slot

Individual probabilities

The probability that the ball lands on a red slot is calculated as:

[tex]p = \frac{18}{38}[/tex]

Simplify

[tex]p= \frac{9}{19}[/tex]

The probability that the ball does not land on a red slot is calculated as:

[tex]q = \frac{18+2}{38}[/tex]

[tex]q = \frac{20}{38}[/tex]

Simplify

[tex]q = \frac{10}{19}[/tex]

Binomial probability

The value of P(R = 3) is then calculated using the following binomial probability formula

[tex]P(R = r) = ^nC_rp^rq^{n-r}[/tex]

Where:

[tex]n = 7[/tex]

[tex]r = 3[/tex]

So, we have:

[tex]P(R = 3) = ^7C_3 \times (9/19)^3 \times (10/19)^{7-3}[/tex]

[tex]P(R = 3) = 35 \times (9/19)^3 \times (10/19)^4[/tex]

[tex]P(R = 3) = 0.2854[/tex]

Hence, the value of P(R = 3) is 0.2854

Read more about probabilities at:

https://brainly.com/question/15246027

Answer: ( 7 3)(18/38)^3(20/38)^3

Step-by-step explanation:

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