annoying probability Q

sd123

okay so my probability knowledge isn't the best so maybe some of you boardies can help me out!


Two dice are thrown. What is the probability of getting at least one 4?

So I said, one four or two fours
p(4) x p(no four) + p(4) x p(4)

This gives (1/6) x (5/6) + (1/6) x (1/6)
= (5/36) + (1/36)
= (1/6)

However the book does it by (1 - probability 4 not occurring)

Which gives 1 - ( 5/6 x 5/6)
= 1- 25/36
= (11/36)

Irish Wolf

Probability was never really my favourite topic so take a look here - it seems to give a fairly comprehensive breakdown...

http://mathforum.org/library/drmath/view/61597.html

MathsManiac

Much easier to just count all the outcomes (using a 6x6 checkbox grid if you like).

However, if you just want to know where your own error was, you need to double the first term in your solution, because it could be (not 4) then 4, as well as 4 then (not 4).

aequinoctium

it would be 2 times p(4)*p(no four) as either of the die could be the 4

this gives: (2)(1/6)(5/6) + (1/6)(1/6)

that is: (10/36) + (1/36) = (11/36)

MathsManiac

By the way, you do all realise, I hope, that if you're only doing core probability, you will never actually have to multiply or add two probabilities?

Every question can be done by counting the total number of outcomes, and counting the outcomes of interest and putting the one over the other.;)

sd123

10 minutes, 3 replies- not too shabby. thanks for that, realy helpful:)

euwwy deuwwy

3 possible outcomes. a 4 and a 4 or a 4 and another or another and a 4 == 1/6x1/6 + 1/6x5/6 + 5/6x1/6 === 11/36. I know this has already been answered but what can I say, I like probability.

ZorbaTehZ

Probability.

cocoa

MathsManiac wrote:

By the way, you do all realise, I hope, that if you're only doing core probability, you will never actually have to multiply or add two probabilities?

Every question can be done by counting the total number of outcomes, and counting the outcomes of interest and putting the one over the other.;)

well, technically yes, but once you've found the speed that is adding and/or multiplying why would you go back?

Tomlowe

i would suggest that when you're answering probability questions, always check to see if your answer makes sense; as in this one, you got the probability of at least one being four as being the same as rolling one four from one roll. clearly its easier to get at least one four from two rolls than one, so your answer doesnt make sense. its a good way to double check answers

md99

arghhh... can never get the multiplying thing. I love the probability Qs where you never need to do this.

JC 2K3

If it says "and" in the question you multiply, easy as that in most cases....