00:01
We start off with a paragraph of information.
00:03
Let's write a probability notation.
00:06
So we have a group of test subjects.
00:08
66 % are successful with their left hands.
00:11
So if you pick someone at random, probability they are successful with their left hands is 0 .66%.
00:18
82 % with their right hands.
00:22
50 % with either.
00:26
So both hands work.
00:32
Now, in part a, what percentage could not operate with either? so i'm going to draw a quick venn diagram.
00:40
Some use their left, right, both, or neither.
00:45
Now if i put in the information here, both goes in the middle, which depends on the percentage, less space.
00:52
So 51 % can use either.
00:54
If you say left or right, both would work.
00:59
Now, some of them can use the left but cannot use the right.
01:05
66%, in total, can use the left, so this entire circle.
01:08
We've got 51 % here, this must be 15%, to get these two add up to 66%.
01:14
This circle adds up to 52%.
01:17
So we've got 51 % here, this must be the other 31%.
01:21
Now if i add all of these up, i can see that we have 97 % in one of these, leaving 3 % outside to bring up to everybody.
01:35
So 3 % cannot use either.
01:38
How's success with right and left hands independent? so independent means they do not affect each other.
01:50
So whether or not you can use one hand does not affect if you can use the other.
01:57
How do you test it? well, if they are independent, the probability of both working would be equal to the probability of the left hand working multiplied by probability of a right hand working...