Question 1176452: Mr. Arnold is a judge at a science fair that contains the following projects: 5 geology, 3 chemistry, 5 physics, and 2 biology projects. The order in which he will judge the projects will be randomized. What is the probability that the first two projects judged are_____?
a. a geology and then a chemistry project (answer: 1/14)
b. a biology and then a physics project (answer: 1/21)
c. two physics projects (answer: 1/3)
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
What do you not understand about this problem? Solving it requires only basic concepts about probability....
a. a geology project AND then a chemistry project are the first two to be judged
There are 15 projects in all; 5 of them are geology, so the probability of judging a geology project first is 5/15.
After that, there are 14 projects left, of which 3 are chemistry; the probability of judging a chemistry project second is 3/14.
Since you want both things to happen (the events are connected by "AND"), you multiply the probabilities.
P(geology first AND chemistry second) = (5/15)(3/14) = (1/3)(3/14) = 1/14
Solve the others the same way:
P(biology first AND physics second) = (?)(?) = ...
P(physics first and physics second) = (?)(?) = ...
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