00:01
So in the given question we are told that a fair coin is flipped five times.
00:07
Fair coin is flipped five times and we are asked about the probability that the first flip comes up head.
00:24
Probability that the first flip comes up head comes up as heads so what we can see is that when we are flipping the coin five times there is a total outcome total number of outcomes is found by two raised to the power the number of times the coin is stripped that is five so we have one zero we have 32 outcomes right have 32 outcomes total outcomes different outcomes is what we have so what we can see is that out of the five out of what we would have is divide this into five columns if the first flip as heads then we can say that this first flip is reserved as head right so out of heads and tails anyone any two one two of any would come over here we have two choices in the second column in third column as well and two outcomes two possible outcomes in the fourth and the fifth flip right so only in the first flip it is necessary that it should show heads and the all other flips can it can be anything else so we could write the probability to be two raised to the power four out of 32 two raised to the power four is 16 it is is 16.
02:38
So 16 out of 32 would give us a probability of 1 by 2.
02:43
Now in the next case we are told to find the probability that exactly 4 heads appears.
02:51
Exactly 4 heads appear.
02:57
So here also we would use the same we can see that when a coin is flipped 5 times the total number of times exactly four heads would happen is only one, two, three, four and five times.
03:31
Only five times does it happen that four, exactly four heads would appear in five flips of a coin.
03:41
So we could write it is five out of 32.
03:45
Next we have the probability that exactly, exactly four heads appear, four heads appear, four heads appear, appear, given that, given that the first flip comes up head, given that, given that the first flip is heads, heads.
04:14
First flip as heads so what we could do over here is that we can simply take the probability from the above sample space itself we can take this a sample from the above sample space itself so this are the outcomes in which four exactly four head appears so the there is only out of 1, 2, 3, 4, 5 outcomes, there is only one outcomes in which the first flip does not give us heads, right? in all the other occurrences where in all the other outcomes where we can see 4 heads, the first flip is head itself.
05:08
So we can write the required probability over here as 4 out of 32...