Conditional probability marble question

In order to have a probability you need to have the number of possible outcomes. The number of outcomes in a) is "the number of blue balls" divided by "the number of non-white balls". That is P(blue| not white)= 3/8. In b) you want "the number of non-red balls" divided by "the number of non-white balls". That is P(not red| not white)= 5/8.In summary, the probability of drawing a blue marble given that the marble drawn is not white is 3/8, and the probability of drawing a non-red marble given that the marble drawn is not white is 5/8.
  • #1
dragon513
26
0
Q. A box contains three blue marbles, five red marbles, and four white marbles. If one marble is drawn at random, find:
a) P(blue|not white)
b) P(not red|not white)

The answer for both a) and b) is 3/8.
However right now I don't even understand the question.

part a) wants possibility of getting a blue ball given that white wasn't drawn.
So... NOT getting a white ball is 8/12.
Given that, getting a blue ball is 3/11.

but 3/11 is not even close to 3/8!

What's wrong with my work?

Thanks in advance!
 
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  • #2
Why not use the defination of conditional probability.
[tex]P(E|F) = \frac {P(E \cap F)} {P(F)}[/tex]
Since the event of getting a blue and non white is the same as saying getting a blue. P(blue) = 3/12 and P(non white) = 8/12

[tex]P (\text{blue} | \text{nonwhite}) = \frac {P(\text{blue})}{P(\text{non-white})} = \frac {\frac {3}{12}}{\frac {8}{12}} = \frac {3}{8}[/tex]
 
  • #3
dragon513 said:
Q. A box contains three blue marbles, five red marbles, and four white marbles. If one marble is drawn at random, find:
a) P(blue|not white)
b) P(not red|not white)
The answer for both a) and b) is 3/8.
However right now I don't even understand the question.
part a) wants possibility of getting a blue ball given that white wasn't drawn.
So... NOT getting a white ball is 8/12.
Given that, getting a blue ball is 3/11.
but 3/11 is not even close to 3/8!
What's wrong with my work?
Thanks in advance!

No, "given that" getting a blue ball is NOT 3/11- you need to take away more than 1 white ball!

Since you are told that the ball drawn was not white, you can just ignore the white ones- it's as if there were no white balls. There were 3 blue, 5 red, and 4 white marbles. Ignoring the white balls, there are a total of 3+ 5= 8 marbles, 3 of which are red.

Of course, since you are ignoring the white balls, saying the ball drawn is NOT blue is exactly the same as saying it is red- the problems in a) and b) are exactly the same.
 

1. What is a "Conditional probability marble question"?

A "Conditional probability marble question" is a type of probability problem that involves selecting marbles from a bag or jar based on certain conditions, such as the color or type of the marble. The goal is to determine the probability of selecting a specific marble or combination of marbles.

2. How do you calculate conditional probability in a marble question?

To calculate conditional probability in a marble question, you first need to determine the total number of marbles in the bag or jar and the number of marbles that meet the given condition. Then, divide the number of marbles that meet the condition by the total number of marbles. This will give you the probability of selecting a marble that meets the given condition.

3. What is the difference between conditional probability and regular probability in a marble question?

The main difference between conditional probability and regular probability in a marble question is that conditional probability takes into account a specific condition, such as the color or type of marble, while regular probability does not. In other words, conditional probability is the probability of an event occurring given that a certain condition is met, whereas regular probability is the probability of an event occurring without any restrictions or conditions.

4. How does the number of marbles in the bag or jar affect the conditional probability in a marble question?

The number of marbles in the bag or jar does not directly affect the conditional probability in a marble question. However, it does affect the total number of marbles that meet the given condition, which in turn affects the probability of selecting a marble that meets the condition. Generally, the more marbles in the bag or jar, the higher the total number of marbles that meet the condition and the higher the conditional probability.

5. Are there any strategies for solving conditional probability marble questions?

Yes, there are several strategies that can be helpful in solving conditional probability marble questions. These include creating a visual representation of the marbles and their colors or types, using tree diagrams to show the different possible outcomes, and breaking the problem down into smaller, more manageable parts. It is also important to carefully read the question and any given information to ensure all conditions are taken into account.

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