SOLUTION: Based on his past baseball history, Kurt has a (n) 15% chance of reaching first base safely, a (n) 7% chance of hitting a double, a (n) 5% chance of hitting a triple. a (n) 5% chan

Question 850818: Based on his past baseball history, Kurt has a (n) 15% chance of reaching first base safely, a (n) 7% chance of hitting a double, a (n) 5% chance of hitting a triple. a (n) 5% chance of hitting a home run, and a (n) 68% chance of making an out at his next at bat.
Determine Kurt's expected number of bases for his next at bat.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
15% change of reaching first.
7% chance of hitting a double.
5% chance of hitting a triple.
5% chance of hitting a home run.
68% chance of making an out.

his expected number of bases would be:

.15*1 + .07*2 + .05*3 + .04*4 + .68*0 which is equal to .64.

his expected number of bases the next time at bat are .64.

what does this mean?

assume he bats 1000 times.

he would be expected to reach a total of .64 * 1000 = 640 bases.

out of the 1000 times at bat, he would:

reach 1st 15% of the time = .15 * 1000 = 150 * 1 base = 150 total bases.
reach 2d 7% of the time = .07 * 1000 = 70 * 2 bases = 140 total bases.
reach 3d 5% of the time = .05 * 1000 = 50 * 3 bases = 150 total bases.
reach 4th (home plate) 5% of the time = .05 * 1000 = 50 * 4 bases = 200 total bases.

add them up and he would have reached 640 total bases after 1000 times at bat.
his average per at bat would be 640 / 1000 = .64.

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