00:01
In this problem, we are given probabilities about when a present is hidden by mom or dad and when it is hidden downstairs or upstairs.
00:10
Now, using this information, we first of all need to find the probability that the present is upstairs.
00:16
So we need to find the probability that it's upstairs.
00:19
Now, there are two situations, either the, either mom hit it or dad hit it.
00:26
So if we consider that the mom hit it, then we will have the probability that mom hit it as probability u given m times p .m.
00:42
This is one of our options.
00:43
And the other option is that the dad hit it.
00:46
So p of u given f, if we consider the dad, the father, we consider the event that it was hit by the father as f, then we have this.
00:55
So this will give us the probability that the present was hidden upstairs.
01:00
So the probability that the present was hidden upstairs given that it was hidden by mom, well, that probability will be 0 .7 because it is said that mom hides it upstairs 70 % of the time.
01:14
And the probability that mom hid it was 0 .6.
01:18
And the probability of you given f will be the probability will be 0 .5 because you given f will be 0 .5 because the dad is equally likely to hide it upstairs or downstairs.
01:33
So there's a 50 -50 chance.
01:34
The probability of it being upstairs will be 50 % of 0 .5.
01:38
And the probability that it was hidden by the father is 0 .4.
01:43
So this is what we get.
01:44
So we have 0 .42 plus 0 .2 and that is equal to 0 .62.
01:51
So the probability that the present is upstairs is 0 .62...