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A jar contains 4 red marbles, numbered 1 to 4, and 11 blue marbles numbered 1 to 11.
a) A marble is chosen at random. If you're told the marble is blue, what is the probability that it has the number 2 on it?
b) The first marble is replaced, and another marble is chosen at random.
If you're told the marble has the number 1 on it, what is the probability the marble is blue?
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It is a conditional probability problem.
(a) There are 11 blue marbles.
The probability that the selected blue marble has the number 2 is . ANSWER
To solve such problems, we reduce the total space of events (4+11 = 15 marbles)
to its smaller sub-space, consisting of 11 blue marbles.
(b) There are 2 marbles with the number 1 on them. They are red and blue.
The probability that the selected marble, marked 1, is blue is . ANSWER
To solve such problems, we reduce the total space of events (4+11 = 15 marbles)
to its smaller sub-space, consisting of 2 marbles, market by number 1.
Solved.
As I said, the method to solve these two problems is the same.
Therefore, I explain the solutions practically in the same words.
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On conditional probability, see the lessons
- Conditional probability problems
- Conditional probability problems REVISITED
- More problems on Conditional probability
in this site.
Read them to develop your skills and knowledge.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Solved problems on Probability"
and "Additional problems on Probability".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.