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Math Help - School Bus

  1. #1
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    School Bus

    On mornings when school is in session in January, Sara notices that her school bus is late one-third of the time. What is the probability that during a 5-day school week in January her bus will be late
    at least three times?

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  2. #2
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    Quote Originally Posted by magentarita View Post
    On mornings when school is in session in January, Sara notices that her school bus is late one-third of the time. What is the probability that during a 5-day school week in January her bus will be late

    at least three times?
    Let X be the random variable number of day the bus is late.

    X ~ Binomial(n = 5, p = 1/3)

    Calculate \Pr(X \geq 3) = \Pr(X = 3) + \Pr(X = 4) + \Pr(X = 5).

    You should have a formula for calculating each of these probabilities.
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  3. #3
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    no.........

    Quote Originally Posted by mr fantastic View Post
    Let X be the random variable number of day the bus is late.

    X ~ Binomial(n = 5, p = 1/3)

    Calculate \Pr(X \geq 3) = \Pr(X = 3) + \Pr(X = 4) + \Pr(X = 5).

    You should have a formula for calculating each of these probabilities.
    No formulas were given in class.
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  4. #4
    Bar0n janvdl's Avatar
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    Quote Originally Posted by magentarita View Post
    No formulas were given in class.
    P(X = k) = {n \choose k} \left( p \right)^k \left( 1 - p \right) ^{n-k}

    Where n would be the total number of days, k the number of successes (3;4;5 in your case), and p the probability the bus is late.
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  5. #5
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    ok...........

    Quote Originally Posted by janvdl View Post
    P(X = k) = {n \choose k} \left( p \right)^k \left( 1 - p \right) ^{n-k}

    Where n would be the total number of days, k the number of successes (3;4;5 in your case), and p the probability the bus is late.
    Thanks for the formula.
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