Probability SAT math level 2 question ?

Question

If the probability that john will buy a certain product is 3/5, that bill will buy that product is 2/3, and that sue will buy that product is 1/4. What is the probability that at least one of them will buy the product?

ok...so here's how I am with this so far.....

Because these events are buying products, they are ofcourse independent events. So, the probability of all of them buying the product is (3/5)(2/3)(1/4)=1/10. So the probability of atleast one of them buying it would be (1)-(1/10)=9/10.

I am stuck here...how do u solve it...is there any general techniques that could make these dependent/independent/,mutually inclusive events problems easier...plz do explain

thanks

much appreciated

Answer 1

Ok I'll first point our your mistake. You first computed the probability that all 3 will buy the product. However the complement of this event is NOT that at least one of them will buy it but rather that not all of them will buy it (i.e. none of them will buy it, 1 of them will buy it, or 2 of them will buy it). Notice how this is not the same as at least one of them will buy it (1 of them buy it, 2 of them buy it, or all 3 of them buy it).

Your instinct to find the probability of the complement is a good one for this problem. However, the complement of at least one of them buying it is actually none of them buy it. This occurs with probability (2/5)(1/3)(3/4) = 1/10. Then, the desired probability is 1 - 1/10 = 9/10. As it turns out you got the correct answer by coincidence although your reasoning wasn't quite right.