Question

This probability distribution shows thetypical distribution of pitches thrown to abatter in a given "at-bat" in a baseball game.Pitchesthrow fewer than 3 pitches to a batter.

Answer 1

Explanation:

From the table, the total sample space will be calculated below as

$n(S)=15+20+40+15+10=100$

Concept:

To calculate the probability of throwing fewer than 3 pitches, we will use the formula

$P(PITCHES<3)=P(1)+P(2)$

The probabaility of throwing 1 pitch is calculated below as

$P(1)=\frac{n(1)}{n(S)}=\frac{15}{100}$

The probabaility of throwing 2 pitches is calculated below as

$P(1)=\frac{n(2)}{n(S)}=\frac{20}{100}$

Hence, by susbtituting the values in the formula, we will have

$\begin{gathered} P(PITCHES\lt3)= P(1)+P(2) \\ P(PITCHES\lt3)=\frac{15}{100}+\frac{20}{100}=\frac{35}{100}=0.35 \end{gathered}$

Hence,

The final answer is

$0.35$