Question Video: Using Probability Tree Diagrams to Decide Whether Events Are Independent | Nagwa Question Video: Using Probability Tree Diagrams to Decide Whether Events Are Independent | Nagwa

Question Video: Using Probability Tree Diagrams to Decide Whether Events Are Independent Mathematics • Third Year of Secondary School

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A bag contains 4 red balls and 3 blue balls. I take one at random, note its color, and put it on the shelf. I then take another ball at random, note its color, and put it on the shelf next to the first ball. The figure below shows the probability tree associated with this problem. Are the events of “getting a blue ball on the first draw” and “getting a red ball on the second draw” independent?

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Video Transcript

A bag contains four red balls and three blue balls. I take one at random, note its color, and put it on the shelf. I then take another ball at random, note its color, and put it on the shelf next to the first ball. The figure below shows the probability tree associated with this problem. Are the events of “getting a blue ball on the first draw” and “getting a red ball on the second draw” independent?

We recall that independent events are not affected by previous events. In this question, we’re looking at getting a blue ball on the first draw and a red ball on the second draw. The probability of getting a blue ball on the first draw is three-sevenths. The probability of getting a red ball on our second draw occurs in two places on the tree diagram. It is three-sixths if we select a red ball first, but four-sixths if we select a blue ball first. This means that getting a blue ball on the first draw does affect the probability of getting a red ball on the second draw.

This means that the correct answer is no, the events are not independent. Had the first ball being replaced instead of being put on the shelf, then the events would be independent as the first draw would not impact the second draw.

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