Question

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?

Answer 1

The value of P(R = 3) is 0.2854

Probability

Probabilities are used to determine the chances of events.

The given parameters are:

• $n = 38$ --- the number of slots
• $red = 18$. --- the number of red slot
• $black = 18$. --- the number of black slot
• $green = 2$. --- the number of green slot

Individual probabilities

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

$p = \frac{18}{38}$

Simplify

$p= \frac{9}{19}$

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

$q = \frac{18+2}{38}$

$q = \frac{20}{38}$

Simplify

$q = \frac{10}{19}$

Binomial probability

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

$P(R = r) = ^nC_rp^rq^{n-r}$

Where:

$n = 7$

$r = 3$

So, we have:

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

$P(R = 3) = 35 \times (9/19)^3 \times (10/19)^4$

$P(R = 3) = 0.2854$

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

Read more about probabilities at:

brainly.com/question/15246027

Answer 2

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

Step-by-step explanation: