# School Bus

• Nov 29th 2008, 09:22 PM
magentarita
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?

• Dec 1st 2008, 02:45 AM
mr fantastic
Quote:

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

You should have a formula for calculating each of these probabilities.
• Dec 2nd 2008, 09:46 PM
magentarita
no.........
Quote:

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

You should have a formula for calculating each of these probabilities.

No formulas were given in class.
• Dec 2nd 2008, 09:53 PM
janvdl
Quote:

Originally Posted by magentarita
No formulas were given in class.

$\displaystyle P(X = k) = {n \choose k} \left( p \right)^k \left( 1 - p \right) ^{n-k}$

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.
• Dec 5th 2008, 12:29 PM
magentarita
ok...........
Quote:

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

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.