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The value of P(R = 3) is 0.2854
Probabilities are used to determine the chances of events.
The given parameters are:
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]
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:
