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Math Help - Traffic Intersection Probability

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    Traffic Intersection Probability

    At a certain intersection, the light for eastbound traffic is red for15 seconds, yellow for 5 seconds, and green for 30 seconds. Find, to thenearest tenth, 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.
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    Quote Originally Posted by magentarita View Post
    At a certain intersection, the light for eastbound traffic is red for15 seconds, yellow for 5 seconds, and green for 30 seconds. Find, to thenearest tenth, 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.
    Probability of a car being stopped by a red light is p = 15/50 = 3/10.

    Let X be the random variable number of cars stopped by a red light.

    X ~ Binomial(n = 8, p = 3/10).

    \Pr(X = 3) = {8 \choose 3} \left(\frac{3}{10}\right)^3 \left(\frac{7}{10}\right)^5 = \, ....
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    ok

    Quote Originally Posted by mr fantastic View Post
    Probability of a car being stopped by a red light is p = 15/50 = 3/10.

    Let X be the random variable number of cars stopped by a red light.

    X ~ Binomial(n = 8, p = 3/10).

    \Pr(X = 3) = {8 \choose 3} \left(\frac{3}{10}\right)^3 \left(\frac{7}{10}\right)^5 = \, ....
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