 Hi friends and how are you all today? The question says, the mean and variance of a binomial distribution are 4 and 4 by 3 respectively. Find probability of x is greater than equal to 1. Now here first let us write down the given values we are given mean that is n into p as 4 and we are given variance that is n into p into q as 4 by 3. Now if we divide let this be the first equation, this be second equation. If we divide the second equation by the first equation we will get the value of q isn't it? So dividing second equation by the first equation we get npq upon np equal to 4 divided by sorry 4 by 3 divided by 4. This implies q is equal to 4 by 3 into 1 by 4 that implies q is equal to 1 by 3. Now further we know that is equal to 1 minus q right. So if q is 1 by 3 then the value of p will be equal to right it will be 2 by 3. Now we have the value of q as well as p so we can find out the value of n we know that mean that is n into p is equal to 4. This implies n into 2 by 3 is equal to 4. This further means n is equal to 4 into 3 by 2 which gives us the value of n as thus we can write down that probability when x is greater than equal to 1 is equal to 1 minus probability that x is equal to 0 which is 1 minus q raised to the power n. Now we know the value of q as well as n so we have the value of q as 1 by 3 the value of n as 6. So this further implies 1 minus the value of 1 by 3 raised to the power 6 comes out to be approximately 0.0014. So we have it like 0.9986 approximately. So probability of x is greater than equal to 1 is 0.9986 approximately right. So this ends the session hope you understood it better enjoy it to have a nice day ahead.