A bag contains five 40-W light bulbs, four 75-W light bulbs, and seven 100-W lig

Question

A bag contains five 40-W light bulbs, four 75-W light bulbs, and seven 100-W light bulbs.

A) If light bulbs are selected one by one randomly, find the probability that at least two light bulbs must be selected to obtain one that is rated 100-W

B) If two light bulbs are selected randomly and at least one of them is found to be rated 75-W, find the probability that both of them are 75-W

C) If two light bulbs are selected randomly at least one of them is not rated 75-W, find the probability that both of them have different ratings.

Explanation / Answer

Ok so if I understand A correctly... you must select at least two light bulbs before you pick the 100W bulb. In that case you can have 40,40...75,75...40,75....75,40 So here we have 5/20*5/20 + 4/20 *4/20 + 5/20*4/20 + 4/20*5/20 = 81/400 now if we pick 3 bulbs we can have 40,40,40 40,40,75 40,75,75 40,75,40 75,75,75 75,40,75 75,75,40 75,40,40 I think that covers all of them. Now! 5/20*5/20*5/20 + ... etc so now we have 81/400 + 1/64+1/80+1/100+1/80+1/125+1/100+1/100+1/80 (this all equals 729/8000) So now we have a geometric sum. The first term is 81/400 and the common ratio in the remaining terms will be 729/8000. The sum of geometric is a/1-r where a is the first term and r is common ratio So 81/400 / 1 - 729/8000 = .2228 and that should be the desired probability.

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