Given that events a and b are independent with p, left bracket, a, right bracket, equals, 0, point, 3, 6p(a)=0.36 and p, left bracket, b, vertical bar, a, right bracket, equals, 0, point, 5p(b∣a)=0.5, determine the value of p, left bracket, b, right bracketp(b), rounding to the nearest thousandth, if necessary.