Airbags are manufactured by aces (a), best (b), and cool (c) at rates of 57%, 26% and 17%, respectively. airbags occasionally kill (k) passengers when they deploy in accidents. airbags made by aces, best, and cool do not kill people at rates of 99%, 96%, and 87%, respectively. one airbag is randomly selected for testing. if an airbag kills a passenger, calculate the probability that the airbag was manufactured by cool. (round to the nearest ten-thousandth.)

Air bag manufactured by Aces(A)=57%

So, Probability

Air bag manufactured by Best (B) =26%

So, Probability

Airbag manufactured by Cool(C)=17%

So, Probability

Airbags made by Aces, Best, and Cool do not kill people at rates of 99%, 96%, and 87%, respectively.

Let K be the event which kill people.

Probability of Air bag made by A which kill people

Probability of Air bag made by B which kill people

Probability of Air bag made by C which kill people

If an airbag kills a passenger, calculate the probability that the airbag was manufactured by Cool

Using Baye's theorem:

Substitute the values of probabilities into formula

We get,

Now we calculate it and get probability

So,

So, 57.85% of passenger kills if the airbag was manufactured by Cool.

practice. practice. practice.