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Hello everyone.
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So in this question we have given sample size n is equal to 4 and probability of success is equal to 0 .10.
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Now we need to find the probability when x is equal to 2, x is equal to 3, x is greater than equal to 2 and x is less than 3.
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So we will find our probabilities one by 1.
00:19
So first of all, we will find the probability when x is equal to 2.
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And we know that by binormal distribution, there is a formula for finding the probability.
00:29
So the formula is the probability that random variable x is equal to a particular value, small x is equal to ncx multiplied by probability of success power x, multiplied by 1 minus probability of success power n minus x.
00:46
And here in our case, n is equal to 4, probability of success is equal to 0 .10, and x is equal to 2.
00:55
So on putting the values into formula, we will get probability of x is equal to 2 is equal to 4c2 multiplied by probability of success is 0 .10 power 2 multiplied by 1 minus 0 .10 power 4 minus 2.
01:17
And we know that ncr can be calculated as n factorial divided by r factorial, multiplied by n minus r.
01:25
So this is the formula for finding the combination.
01:29
So using the combination formula we can find 4c2 value that is 4 factorial divided by 2 factorial multiplied by 4 minus 2 is 2 factorial.
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Then multiplied by 0 .10 power 2 multiplied by 1 minus 0 .10 is 0 .90 power 2.
01:48
So now 4 factorial can be written as 4 multiplied by 3 multiplied by 2 factorial divided by 2 factorial, multiplied by 2 factorial is 2, multiplied by 0 .10 power 2, multiplied by 0 .90 power 2.
02:05
So here we can cancel 2 factorial from numerator and denominator, and on solving this we will get equal to 0 .1651.
02:14
Now moving forward to the second part of the question, here we need to find the probability when x is equal to 3.
02:22
So when x is equal to 3, then we will use the probability distribution formula, that is probability of x is equal to 3.
02:33
So this is equal to 4c3 multiplied by probability of success is 0 .10 power 3 multiplied by 1 minus 0 .10 power 4 minus 3.
02:45
So now we can find 4c3 using the combination formula, which is 4 factorial divided by 3 factorial.
02:52
Multiplied by 4 minus 1 is 1 factorial multiplied by 0 .10 power 3 multiplied by 0 .90 power 1...