two maths problems

real_arsen_ac · Posted: Wed Jul 23, 2008 6:51 am Post subject: two maths problems

Hey guys, i got 2 problems here in OG:

1.The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to tossed 3 times, what is the probability that on at least one of the tosses the coin will turn up tails?
a.1/8 b.1/2 c.3/4 d.7/8 e.15/16
the answer is d

2.In a nationwide poll, N people were interviewed. If 1/4 of them answered yes to question 1, and of those, 1/3 answered yes to question 2, which of the following expressions represnets the number of people interviewed who did not answer yes to both questions?
a.N/7 b.6N/7 c.5N/12 d.7N/12 e.11N/12
the answer is e

VP_Tatiana · Posted: Wed Jul 23, 2008 7:35 am Post subject:

Problem 1:
We have 2 outcomes for each toss, so in all there are 2^3=8 outcomes. There is only one outcome in which we don't get tails at least once, the outcome where we have heads, heads, heads. So, in 7/8 outcomes we get tails at least once.

Problem 2:
Since we're dealing with 1/4 and 1/3, let's pick 12 to represent the number of people interviewed since it is a nice round number. Out of those people, 1/4 said yes to question 1. So, 3 people said yes. Out of those, 1/3 said yes to question 2. So, 1 person said yes to both question 1 and question 2. Since there were 12 people total, 11/12 did not say yes to both questions.