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Hello everyone.
00:02
So the event is tossing a fair coin with success in the question a in the part a b, c we have to find the probability that number of heads is less than between or equal to.
00:16
So the random variable x is defined as number of heads.
00:25
Probability of success, that is probability of getting head becomes 0 .5 and probability of failure, q, which is probability of getting not getting it, that is probability of getting tail, which is 0 .5, which can also be written as q is equals to 1 minus.
00:48
Now, we see that hair x is a binomial distribution with parameters n, which is given to be thousand flips, and probability of success p is equals to 0 .5.
01:03
So, the probability mass function, probability of x is equal to small x for binomial distribution is ncx, p raised to the power x, q raised to the power n minus x.
01:19
So using this, let us come to part a.
01:23
What is the probability that number of heads is less than 460? probability that x is less than 460.
01:31
So, this will be summation over x from 0 to 459.
01:42
N is 1000, so 1000 cx p is 0 .5 raised to the power x x multiplied by 0 .5 raised to the power 1000 minus x.
01:59
Here the values of x will be 0 1, 2, so on till 459...