The records of a hospital show that `10%` of the cases of a certain disease are fatal. If `6` patients are suffering from the disease, then the probability that only three will die is

Options

A. `8748xx10^(-5)`
B. `1458xx10^(-5)`
C. `1458xx10^(-6)`
D. `41xx10^(-6)`

Answer

B

Explanation

The probability of suffering of a diseases is 10 %
` p = ( 10) /( 100 ) = ( 1 ) / ( 10 ) `
` and q = ( 9 ) /( 10) `
Total number of patients `n = 6 `
` therefore ` Required probability
` = ""^ 6 C _ 3 (( 1 ) /( 10) ) ^ 3 ((9 ) /( 10)) ^ 3 `
` = ( 6 * 5 * 4 ) /( 3 * 2 * 1) xx ( 1 ) /( 1000) xx ( 9 xx 9 xx 9 ) /( 1000) `
` = ( 2 ) /( 10 ^5) xx 729 = 1458 xx 10 ^( - 5 ) `