In a football game, after a touchdown has been made, the scoring team can just k

Question

In a football game, after a touchdown has been made, the scoring team can just kick a 1 point field goal, or it can try for a 2 point conversion. Suppose that 95% of the time, the team just attempts a field goal. Let there be a 95% chance that the attempt succeeds for 1 point and a 5% chance that there will be no score. Suppose that for the 2 point conversion attempt, it will succeed 40% of the time and fail 60% of the time

Fill in the values to the following tree diagram. (use 2 to 4 digits).

.AA =                     .CC =                     .GGGG =

                               .DD =                     .HHHH =

            .BB =                     .EE =                      .IIII   =

                               .FF =                      .JJJJ =

a. What is the probability that there will be a score after a touchdown (1 or 2 points)?

P(1 or 2 pt score) =

b. What is the probability that there will be a 1 point score?

P(1 pt score) =

c. Given that there is no score after a touchdown, what is the probability that it was a failed 2 point conversion attempt?

P(no 2pt conversion score | no score) =

Explanation / Answer

a) probability that there will be a score after a touchdown =P( try for field goal and succed+try for 2 point coversion and succeed) =0.95*0.95+0.05*0.4 =0.9225

b)probability that there will be a 1 point score =P( try for field goal and succed) =0.95*0.95=0.9025

c) probability of no score =1-P(  probability that there will be a score after a touchdown )

=1-0.9225 =0.0775

therefore   P(no 2pt conversion score | no score) =P(try for 2 point coversion and failed)/P(no score)

=0.05*0.6/0.0775=0.3871

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