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2 years ago

Can someone please help

Mathematics

1 answer:

MissTica2 years ago

7 0

Answer:

I'm Sure You Got The Answer Your Smart

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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,

Elina [12.6K]

The value of P(R = 3) is 0.2854

<h3>Probability</h3>

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

<h3>Individual probabilities</h3>

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

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

<h3>Binomial probability</h3>

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