Respuesta :
The Probability of red light is 0.3
P(red) = 0.3
The probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light be 0.25.
P(exactly three get stopped by red light)=0.25
The correct option is (d) P(red)=.3,P(exactly 3 get stopped)=.25
What is Binomial distribution?
A binomial distribution can be thought of as simply the probability of a SUCCESS or FAILURE outcome in an experiment or survey that is repeated multiple times.
The occurrence,
- Red light= 15 sec,
- Yellow light= 5 sec,
- Green light= 15 sec
p= probability of a red light
=[tex]\frac{15}{15+5+30}[/tex]
= [tex]\frac{15}{50}[/tex]
= 0.3
Hence, Probability of getting red light be,
P (red)= 0.3
Now, the Binomial distribution formula,
Probability=( [tex]_r^nC[/tex])[tex]\;p^{r} \;q^{n-r}[/tex]
where, r = number of times for a specific outcome within n trials
[tex]_r^nC[/tex] = number of combinations
p = probability of success on a single trial
q = probability of failure on a single trial
n = number of trial
According to question,
- r= 3 (Exactly three)
- n=8 (eight eastbound)
- p(red) =0.3
- q= 1 -p
= 1- 0.3
= 0.7
Now using the formula, ( [tex]_r^nC[/tex])[tex]\;p^{r} \;q^{n-r}[/tex]
P( exactly 3 get stopped) = ( [tex]_3^8C[/tex])[tex]\;(0.3)^{3} \;(0.7)^{8-3}[/tex]
= [tex]\frac{8!}{3!(8-3)!}[/tex] [tex](0.027) \; (0.7)^{5}[/tex]
= [tex]\frac{8!}{3!(5)!}[/tex][tex](0.027) \; (0.16807)[/tex]
= [tex]\frac{8 * 7 * 6 }{3 * 2}[/tex] x 0.027 x 0.16807
= 56 x 0.00453789
= 0.25412184
≈ 0.25
Hence, Probability of next eight eastbound so that exactly three will stopped by a red light be 0.25.
Learn more about Binomial distribution here:
https://brainly.com/question/13634543
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