00:01
In an experiment where we flip two fair coins, the sample space is as shown here.
00:08
The sample space is all of the possible outcomes.
00:11
So the first outcome in the sample space indicates that the first coin was ahead and the second coin was ahead.
00:19
The second outcome indicates that the first coin was ahead and the second one was a tail.
00:24
So there are four possible outcomes.
00:28
And for part a we are asked to find two independent events, which we would be asked to find two independent events, we will call a and b from this experiment.
00:38
Two events that are independent means that the outcome for one has no bearing whatsoever on the outcome for the other and vice versa.
00:48
So for example, the event that i sneeze in the next minute and the event that it's going to rain tomorrow are independent events.
00:57
It doesn't matter whether i sneeze or not in the next minute.
01:00
It's not going to affect the weather tomorrow and vice versa.
01:04
So here is one idea for two events that are independent.
01:08
For a we could say the first coin is a tail.
01:15
And for b, we could say the second coin is a tail.
01:22
So what is the probability that the first coin is a tail? there's two possible outcomes that constitute this event.
01:31
Actually it's the other two, not these two.
01:36
So in this outcome, the first is a tail and in this outcome the first is a tail.
01:41
So this probability is 2 out of 4, or half.
01:47
Half of the times that we flip two fair coins, the first one will be a tail.
01:54
Now for event b, the second coin is a tail.
01:57
The number of outcomes that satisfy that are these two...