Probability

[rosie123]

When the KCI Senior Boys Football team has possession of the ball, the following empirical probabilities have been determined:  The probability that the quarterback completes a pass is 0.6  The probability that the quarterback completes a pass and they score a touchdown is 0.01 Find the probability that they score a touchdown given that the quarterback completes a pass.

 

[tkhunny]

p(doesn't complete a pass)?

 

[rosie123]

The answer is supposed to be 1.66%. I just don't know how to get it

 

[Harry_the_cat]

When the KCI Senior Boys Football team has possession of the ball, the following empirical probabilities have been determined:  The probability that the quarterback completes a pass is 0.6  The probability that the quarterback completes a pass and they score a touchdown is 0.01 Find the probability that they score a touchdown given that the quarterback completes a pass.

I find it easier to do these questions by getting rid of all the non-mathematical information in the wordy question and use probability notation.

Let A represent the statement "quarterback completes a pass " - then we can say that P(A) = 0.6.
Let B represent the statement "they score a touchdown" - we are not given P(B).

"The probability that the quarterback completes a pass and they score a touchdown is 0.01" can be written as P(A\(\displaystyle \cap\)B) = 0.01.

"Find the probability that they score a touchdown given that the quarterback completes a pass"ie you need to find P(B | A).

Now go to the formulae you have learnt and see if you can piece it together. Show us what you have tried.

 

[Harry_the_cat]

Did you solve it?

 

[Romsek]

Applying post #4

[MATH]P[\text{score TD | completion}] = \dfrac{P[\text{score TD and completion}]}{P[\text{completion}]} = \dfrac{0.01}{0.6} = 0.01\bar{6} \approx 1.67\%[/MATH]