Question

Poor Milhouse is hopelessly in love with Lisa. Unfortunately for Milhouse, Lisa does not feel the same way. However, Milhouse remains hopeful, since on any given day independently there is a 6% chance that Lisa smiles at him. (Assume a month has 30 days for this problem.) What is the probability that Milhouse goes longer than a month without a smile from Lisa

Answer 1

Answer:

15.6%

Step-by-step explanation:

Since each day there is a 6% chance that Lisa smiles at him then that means that each day there is a 94% chance that Lisa does not smile at him. To find the probability of Milhouse going longer than a month (30 days) without a smile from Lisa we need to multiply this percentage in decimal form for every day of the month. This can be solved easily by putting 94% to the 30th power which would be the same, but first, we need to turn it into a decimal...

94% / 100 = 0.94

$0.94^{30}$ = 0.156

Now we can turn this decimal into a percentage by multiplying by 100

0.156 * 100 = 15.6%

Finally, we can see that the probability that Milhouse goes longer than a month without a smile from Lisa is 15.6%