SOLUTION: You order fourteen hot dogs from a restaurant, eight with onions, six without. If the hot dogs are not labeled and you pick four at random, find the probability of each of the fol

Algebra ->  Probability-and-statistics -> SOLUTION: You order fourteen hot dogs from a restaurant, eight with onions, six without. If the hot dogs are not labeled and you pick four at random, find the probability of each of the fol      Log On


   

Question 323883: You order fourteen hot dogs from a restaurant, eight with onions, six without. If the hot dogs are not labeled and you pick four at random, find the probability of each of the following:
a. None has onions.
b. At least one has onions.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
You order fourteen hot dogs from a restaurant, eight with onions, six without. If the hot dogs are not labeled and you pick four at random, find the probability of each of the following:
a. P(None has onions) = 6C4/14C4 = 15/1001 = 0.015
----------------------------
b. P(At least one has onions) = 1-P(none has onions) = 1-0.015 = 0.985
====================
Cheers,
Stan H.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


a. You want the probability of 0 successes out of 4 trials where the probability of success on an individual trial is eight with onions out of 14 total which is .

The probability of successes in trials where is the probability of success on any given trial is given by:



Where is the number of combinations of things taken at a time and is calculated by

So:



You get to do your own arithmetic. Hint: and

b. At least one has onions is every other possibility except what you just calculated in part a. Therefore the desired probability is exactly 1 minus the result of part a.

John