Question 1099537: A bag contains 200 balls that are either red or blue and either dull or shiny. There are 55 shiny red balls, 91 shiny balls, and 79 red balls. If a ball is chosen at random, what is the probability that it is either a shiny ball or a red ball? What is the probability that it is a dull blue ball?
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! In this problem, you must make sure to avoid double counting. In the first question, when we compute the probability that a ball is red, we have already counted both the shiny red balls and the dull red balls. Thus, when we compute the probability of getting a shiny ball, we must only consider the ones that are blue since the shiny red ones were already counted.
Thus P(red or shiny) = P(red) + P(shiny blue)
P(red) = 79/200
The number of shiny blue balls is 91 - 55 = 36
P(shiny blue) = 36/200
So P(red or shiny) = (79+36)/200 = 0.575
The number of dull blue balls = 200 - 79 - 36 = 85
Therefore P(dull blue) = 85/200 = 0.425
Notice that the two probabilities add to 1, as they should since a ball is either red, shiny blue, or dull blue
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