Probability problems?

Q)a box contains 2 white balls,3 black balls and 4 red balls. the number of ways in which 3 balls can be drawn from the box so that atleast one of the balls is black is


A) 74


B) 64


C) 94


D) 20


E) 24





Q)A box contain 10 bulbs, out of which 2 are defective. 3 bulbs r choosen at random frm this box.the probability that atleast one of these is defective.








can someone give me the answers and explain how to do such problems?

Probability problems?
Quickest way to count "at least one" is to count how many ways to get 0 and subtract from total ways.


9 total balls, 3 are black, 6 are not. #ways to get 0 is 6C3 = 20, #total ways to choose 3 balls is 9C3 = 84, so #ways at least one black is 84-20 = 64


Bulbs work out similarly. #at least 1 defective = 10C3 - 8C3. So prob = this number divided by 10C3.
Reply:THE FIRST QUESTION IS B AND I DONT KNOW THE SECOND ONE
Reply:q1


2w, 3b, 4r = 9 in all


at least 1 black is needed





more than none black


= 9C3 - 3C0*6C3


= 84 - 1*20


= 64 %26lt;--ans : B





q2


P(defective) = 2/10


P(good) = (10-2)/10 = 8/10





P(at least 1 defective)


= 1 - P(none defective)


= 1 - 8C3/10C3


= 1 - 7/15


= 8/15
Reply:find the number of ways that no balls are black and subtract from the total number of ways





there are 6 balls that are not black


(6*5*4)/3! = 20





the total number of ways is (9*8*7)/3! = 84


84 - 20 = 64








same process.


P (at least 1 is defective) = 1 - P(none is defective)


P = 1 - (8/10)(7/9)(6/8)


P = 8/15
Reply:In the first question you need to know the following.





If you have n objects and chose r of them, the number of combinations is:


n! / ( r! (n-r)! )


this can be written as nCr





there are 9C3 = 84 total ways of getting three balls


there are 6C3 = 20 ways to get three balls without a black ball





answer is 64.





----------------





to get no defects out of the 10 when picking three is:


8/10 * 7/9 * 6/8 = 0.4666667





so to have at least 1 defect is 1 - 0.4666667 = 0.5333333

song words