Video Transcript
A bag contains five red candies and
four blue candies. I take one at random, note its
color, and eat it. I then do the same for another
candy. The figure below shows the
probability tree associated with this problem. Are the events of getting a blue
candy first and getting a red candy second independent?
We know that two events are
independent if the incidence of one event does not affect the probability of the
other event. If the incidence of one
effect [event] does affect the probability of the other event, then
the events are dependent.
In this question, we are interested
in the events of getting a blue candy first and a red candy second. The probability of getting a blue
candy first is four-ninths. The probability of getting a red
candy second has two posssible values, four-eighths and five-eighths. This means that this is affected by
the first candy. If the first candy is red, then the
probability the second candy is red is four-eighths, whereas if the first candy is
blue, the probability the second candy is red is five-eighths.
We can therefore conclude that the
correct answer is no. The events of getting a blue candy
first and getting a red candy second are not independent.
