Question

There is a 60% that your math teacher will give a pop quiz tonight and, due to the fact that you have a soccer game, there is an 85% chance you will not be able to do your math homework. You decide that you will do the homework if the probability of there being a pop quiz and your not doing your homework is greater than 60%. What do you do and why?

Answer 1

Since these are 2 independent events. The probability that both occur is the product of each probability.

0.6*0.85 = 0.51 = 51%

This is less than 60% , so you do NOT do your homework.

Answer 2

Explanation:

Let A be the event that your math teacher will give a pop quiz tonight

and B the event that you have a soccer game

GIven that P(A) = 60% = 0.60

P(B)=85% =0.85

We have A and B are independent since pop quiz and soccer game have no association

Hence P(AB) = P(A) P(B)

THus probability for both pop quiz and soccer game = 0,60(0.85)

=0.51

Obviously 0.51 <0.60

So you need not do the homework