probability help???????????????????????????????

Test Preparation
1

<p>A junk box in your room contains a dozen old batteries, five of which are totally dead. You start picking batteries one at a time and testing them. Find the probability of each outcome.</p>

<p>A.) At least one of the first three works.
B.) The first four you pick all work
C.) You have to pick 5 batteries in order to find that works.</p>

2

<p>An apparently trivial identity:</p>

<p>probability<em>of</em>success + probability<em>of</em>failure = 1</p>

<p>serves to make apparently difficult probability problems easy.</p>

<p>Take (A):</p>

<p>What’s the probability that “none” of the batteries picked in three attempts work?</p>

<p>The probability is 5/12 for the first, 5/12 for second and 5/12 for the third. So (5/12)^3 that none of the three work. So the probability that at least one works is 1 - (5/12)^3</p>

<p>Now (B)</p>

<p>The probability that the first works is 7/12. The same individually for the second, third and fourth. So the probability that all 4 work is (7/12)^4.</p>

<p>And (C)</p>

<p>There’s a likely typo in your transcription. I assume that you mean “1” that works. If so than your first 4 don’t work, and the fifth does. The probability of 4 consecutive failured batteries is (5/12)^4. The probability that the fifth works is (7/12). Multiply the two numbers to get the answer.
(5/12)^4</p>

3

<p>I have to disagree with the above post because I assume that it is not allowed to place butterflies back to the junk box.

  1. If you are unlucky enough, you pick three dead butterflies in a row. The probability is 5/12 times 4/11 times 3/10, giving you 1/22. Then you subtract 1/22 from 1.
  2. Same concept, the probability is 7/12 times 6/11 times 5/10 times 4/9, which gives you 7/594
  3. Again, if you are unlucky enough, you will pick 5 dead butterflies in a row, the probability is 5/12 times 4/11 times 3/10 times 2/9 times 1/8<br>
    I may be wrong.</p>
4

<p>forthesakeofedu – you are right.</p>

<p>I didn’t think through my reply with enough care. </p>

<p>You don’t return batteries to the junk pile, so that every time you take one out there are fewer remaining. You have to take the fewer numbers into account in computing the probability for the second, third etc. pick.</p>