A baseball player has a batting average of 030 Suppose that

A baseball player has a batting average of 0.30. Suppose that you observe successive at-bats of the player and note for each at-bat whether the player gets a hit. Presume that the assumption of Bernoulli trials is appropriate. What is the expected number of trials before the third hit? (Round to an appropriate integer)

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A baseball player has a .345 batting average. [He gets a hit thisfraction of times that he comes to bat.]

If he comes to bat 4 times in a game, what is theprobability he gets exactly 3 hits? 1

What is the expected value for the number of hits he will get in4 times at bat?

answers

A baseball player has a .345 batting average. [He gets a hitthis fraction of times that he comes to bat.]
probability that he wont hit = 1- 0.345 = 0.655
If he comes to bat 4 times in a game, the probability he getsexactly 3 hits =  .345 x .345 x .345 x 0.655 = 0.027

the expected value for the number of hits he will get in 4times at bat (i.e sum of 0 hit, 1 hit, 2 hit, 3 hit or 4 hit)

=(0.655 x 0.655 x 0.655 x 0.655) + (0.655 x 0.655 x 0.655 x .345) + (0.655 x 0.655 x .345 x .345)+ ( .345 x .345 x .345 x0.655 ) + ( .345 x .345x .345 x .345)

=0.184 +0.097 +0.0511 +0.0265 + 0.0142

=0.3728