 # probability problem

A company produces basic digital cameras and luxe digital cameras. Last year 40% of sold digital cameras were the basic ones. You choose randomly 2 buyers. What is the probability that al least one of them has bought a luxe digital camera??

6/10*6/10?

My guess would be 6/10 * 1/2 = 30%

soxboys21 Wrote: ------------------------------------------------------- > My guess would be 6/10 * 1/2 = 30% Duh! I’m a moron.

Why not: (.6)(.4) + (.4)(.6) + (.6)(.6) = 84%?

I think it is 84%. Probability of at least one is probability of one buying plus probability of both buying the lux camera: [2!/(2!*0!)]*0.6^2*0.4^0 + [2!/(1!*1!)]*0.6^1*0.4^1=84%

Simple. Probability that None has a Luxe = .4*.4 Now just take 1- that probability. 1-.4*.4 = .84

KJH Wrote: ------------------------------------------------------- > soxboys21 Wrote: > -------------------------------------------------- > ----- > > My guess would be 6/10 * 1/2 = 30% > > > Duh! I’m a moron. Maybe not, based on the explanations above…

I treated this one like you would treat a coin flip? But I guess it is not independent outcomes. Blasted quant.

P(Digital)=0.60, P(Basic)=0.4 2 Choose 2 = 2!/2! * 0! (0.60)^2 (0.40)^0 = 0.36 2 Choose 1 = 2!/1! * 1! (0.60)^1 (0.40)^1 = 0.48 =0.84

p(at least 1 digital) = 1 - p(both basic) = 1 - 0.4 * 0.4 = .84 easier to solve with the double negative approach for this kind of question. cp

They are independent, just not mutually exclusive. Your original answer was the probability that both person 1 and person 2 bought the luxe camera. This is just one of the cases, as Topher pointed out. Add the other 2 cases, Person 1 buys and Person 2 doesn’t (0.6)(0.4) and Person 2 buys and Person 1 doesn’t (0.4)(0.6) you get 0.84 but blackbelt’s way is easiest!

The question does not exclude the fact that each buyer may have bought both a basic and a lux. What do you say now?

P(A): first buyer P(B): second buyer since it says at least we can use P(AorB)=P(A)+P(B)-P(AB)=0.6+0.6-0.36=0.84

^^^^Great explanation! Makes perfect sense now!

Thank you guys, the answer actually is 84%, so, thanks again!!!

Dreary Wrote: ------------------------------------------------------- > The question does not exclude the fact that each > buyer may have bought both a basic and a lux. > What do you say now? Actually, it doesn’t include the possibility that I bought all the basic ones and all 10,000 other buyers, recognizing that the basic model was a piece of crap, bought the luxe model. The probability is thus 9999/10000.

JoeyDVivre Wrote: ------------------------------------------------------- Actually, it doesn’t include the possibility that I bought all the basic ones and all 10,000 other buyers, recognizing that the basic model was a piece of crap, bought the luxe model. The probability is thus 9999/10000. @Joey: :-), I like your humour @dreary I want to excuse me for our last conversation. I wasn’t a gentleman, sorry.

All in good spirit, cfaisok.

Probability of BOTH buying a Basic one = 0.4*0.4 = 0.16 Probability of AT LEAST ONE buying a Luxe one = 1 - Probability of BOTH buying a Basic one = 1 - 0.16 =0.84 took me a bit of time to think it out though … darn…