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# Independent & dependent probability

Video transcript

The marching band is holding a
raffle at a football game with two prizes. After the first ticket is pulled
out and the winner determined, the ticket is
taped to the prize. The next ticket is pulled out to
determine the winner of the second prize. Are the two events
independent? Explain. Now before we even think about
this exact case, let's think about what it means for events
to be independent. It means that the outcome of one
event doesn't affect the outcome of the other event. Now in this situation, the first
event-- after the first ticket is pulled out and the
winner determined-- the ticket is taped to the prize. Then the next ticket is pulled
out to determine the winner of the second prize. Now, the winner of the second
prize-- the possible winners, the possible outcomes for the
second prize, is dependent on who was pulled out for
the first prize. You can imagine if there's
three tickets, let's say there's tickets A, B,
and C in the bag. And for the first prize,
they pull out ticket A. That's for the first prize. Now, when we think about who
could be pulled out for the second prize, it's only going
to be tickets B or C. Now the first prize could
have gone the other way. It could have been
A, B, and C. The first prize could have
gone to ticket B. And then the possible outcomes
for the second prize would be A or C. So the possible outcomes for
the second event, for the second prize, are completely
dependent on what happened or what ticket was pulled out
for the first prize. So these are not independent
events. The second event-- the outcomes
for it, are dependent on what happened in
the first event. So they are not independent. The way that we could have
made them independent is, after the first ticket was
pulled out, if they just wrote down the name or something,
and then put that ticket back in. Instead they taped
it to the prize. But if they put that ticket
back in, then the second prize, it would have still had
all the tickets there. It wouldn't have mattered who
was picked out in the first time because their name was just
written down, but their ticket was put back in. And then you would have
been independent. So if you had replaced the
ticket, you would have been independent. But since they didn't replace
the ticket, they taped it to the prize, these are not
independent events.