Question

A high school baseball player has a 0.16 batting average. In one game, he gets 8 at bats. What is the probability he will get at least 2 hits in the game?

Answer 1

In order to find the probability of getting at least 2 hits, let's calculate the probability of getting 0 and 1 hit, then we find the complementary probability.

We can calculate the probability of x hits using the formula below:

`P(n,x)=C(n,x)\cdot p^x\cdot(1-p)^(n-x)`

Using n = 8, x = 0 and p = 0.16, we have:

`\begin{gathered} P(8,0)=C(8,0)\cdot0.16^0\cdot0.84^8\\ \\ P(8,0)=1\cdot1\cdot0.84^8\\ \\ P(8,0)=0.247876 \end{gathered}`

Now, let's use x = 1 instead, to find the probability of hitting exactly one time:

`\begin{gathered} P(8,1)=C(8,1)\cdot0.16^1\cdot0.84^7\\ \\ P(8,1)=8\cdot0.16\cdot0.84^7\\ \\ P(8,1)=0.377716 \end{gathered}`

Adding these two probabilities, we have the probability of hitting less than 2 times:

`P(x<2)=P(1)+P(2)=0.247876+0.377716=0.625592`

The complementary probability is the probability of hitting at least 2 times:

`P(x\geq2)=1-P(x<2)=1-0.625592=0.374408`

Therefore the required probability is 0.3744 or 37.44%.