# Math Help - School Bus

1. ## 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?

2. Originally Posted by magentarita
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.

3. ## no.........

Originally Posted by mr fantastic
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.

4. Originally Posted by magentarita
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.

5. ## ok...........

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

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.