An automobile plant contracted to buy shock absorbers from two suppliers $ X$ and $ Y$ . $ X$ supplies $60\%$ and Y supplies $40\%$ of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of $ X’s$ shock absorbers, $96\%$ are reliable. Of $ Y’s$ shock absorbers, $72\%$ are reliable.
The probability that a randomly chosen shock absorber, which is found to be reliable, is made by $Y$ is