Frequently Asked Questions...
A ball is chosen at random from a bag containing 150 balls that are either red or white?
A ball is chosen at random from a bag containing 150 balls that are either red or white and either dull or shiny. There are 36 red shiny balls and 54 white balls.
What is the probability of the chosen ball being shiny conditional on it being red?
What is the probability of the chosen ball being dull conditional on it being red
Answer:
Well we start off with what we know:
54 whites
96 reds
36 shiny reds
60 dull reds.
We don't know how many of the whites are shiny or dull.
Now for the first question... there are 96 total red balls... so once we have a red one the chance it's shiny is 36/96 which is the same as 3/8 = 0.375 or 37.5%
Likewise, if it's known to be red the chance it's dull will be 60/96 which is 5/8 or 62.5%.
This second bit is very easy after the first bit because we know that a red ball is EITHER dull or shiny. So it the probability of a ball being shiny is 0.375 then the chance it's dull has to be 0.625 to make the sum up to 1.
Bag Ball
Ball Bag
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