The probability that an event A happens in one trial of an experiment, is 0.4 There independent trials of the experiments are performed. The probability that the event A happens atleast once, is

Options

A. `0.784`
B. `0.936`
C. `0.964`
D. none of these

Answer

A

Explanation

`p=0.5,q=(1-0.5) =0.6 ` and n=3
Required probability =P( E occuring at least once)
`=.^(3)C_(1).(0.4)^(1) xx(0.6)^(2) +.^(3)C_(2).(0.4)^(2) xx(0.6)^(1)+.^(3)C_(3).(0.4)^(3)`
`=((54)/(125) +(36)/(125)+(8)/(125)) =(98)/(125) =0.784`