Probability of R1 & R2: Solve w/ Tree Diagram

In summary, the conversation discusses the events R1, R2, B2, and G3 which represent the probability of drawing certain colored balls from a bag without replacement. The question asks for the probability of R1 and R2 occurring together as well as the probability of either R1 or R2 occurring. The answer is found by using a tree diagram or by subtracting the probability of both not occurring from 1.
  • #1
crays
160
0
Hi, i have this question
A bag contains 5 red balls, 10 blue balls and 15 green balls. Three balls are drawn from the bag one after another without replacement. The event R1 , R2 , B2 and G3 are defined as follows.

R1 - represents the event the first ball drawn is red.
R2 - represents the event the second ball drawn is red.
B2 - represents the event the second ball drawn is blue.
G3 - represents the event the third ball drawn is green.

Find
a) i) P(R1 [tex]\cap[/tex] R2)

for this , i drew a tree diagram, for it to be red for the first ball, it has to be 5/30 and for the second to be red it has to be 4/29 thus multiplying them both would give me the answer which is 2/87.

ii) P(R1 [tex]\cup[/tex] R2)

for this i thought of P(R1) + P (R2) - P(R1 [tex]\cap[/tex] R2) would solve the problem but the answer is incorrect and later i see, i don't really know what's the probability of R2 because it could be 5/29 or 4/29.

Please help.
 
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  • #2
You see the problem correctly. You could add up the separate cases i) first red, second not red, ii) first not red, second red and iii) both red. But it might be easier to notice that is equal to 1-(first not red)*(second not red).
 
  • #3
You have this on another part of this site - look over there.
 

Related to Probability of R1 & R2: Solve w/ Tree Diagram

What is a tree diagram?

A tree diagram is a visual representation of all the possible outcomes of an event. It consists of branches that show different paths or scenarios that could occur.

How do you calculate the probability using a tree diagram?

To calculate the probability using a tree diagram, you need to multiply the probabilities along each branch of the tree. This will give you the overall probability of the event occurring.

What is the difference between independent and dependent events in a tree diagram?

In an independent event, the outcome of one event does not affect the outcome of the other event. In a tree diagram, this would be represented by branches that are not connected. In a dependent event, the outcome of one event does affect the outcome of the other event, and the branches would be connected in the tree diagram.

How do you know when to use a tree diagram for probability?

A tree diagram is best used when there are multiple steps or events involved in an experiment or situation. It helps to visualize all the possible outcomes and calculate the probability of a specific outcome.

Can a tree diagram be used for more than two events?

Yes, a tree diagram can be used for any number of events. Each additional event would be represented by a new branch on the tree, making it a useful tool for calculating the probability of complex situations.

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