Fireworks manufacturing is a delicate process dependent on complex arrangements of chemicals. Currently, a factory is able to achieve perfect results in 43 out of 47 Sparky fireworks produced.
The company orders a purer type of magnesium which improves their perfect results by 1.15%. What is the probability of producing a perfect Sparky firework now? Express your answer as a decimal rounded to the nearest thousandth
First, let's find the probability of producing a perfect Sparky firework before ordering the purer type of magnesium:
P(perfect without purer magnesium) = 43/47
Now, let's calculate the probability of producing a perfect Sparky firework after ordering the purer type of magnesium:
P(perfect with purer magnesium) = 43/47 + 1.15% of 43/47
P(perfect with purer magnesium) = 43/47 + 0.0115 * 43/47
P(perfect with purer magnesium) = 43/47 + 0.0115
P(perfect with purer magnesium) = 0.9149
Therefore, the probability of producing a perfect Sparky firework after ordering the purer type of magnesium is 0.9149.