Chapter 13.4, Problem 9PPS

To determine

To calculate:

The probability of given event.

Answer to Problem 9PPS

The probability that a baseball player hits an single is $70\%$ , for double is $15\%$ , for triple is $10\%$ , and for an home run is $5\%$ .

Explanation of Solution

Given information:

Event:

According to a baseball players on basr percentages he gets a single $60\%$ of the time, a double $25\%$ of the time, a triple $10\%$ of the time, and a home run $5\%$ of the time.

Calculation:

The following table represents the percentage of on base hits:

Best Hits	Percentage of Tickets
Single	$60\%$
Double	$25\%$
Triple	$10\%$
Home Run	$5\%$

To simulate the players on base hits and estiamate the probability of hits for each type, use a random number generator to generate integers from $1-20$ .

Generate $20$ integers, and let the integers from $1-12$ represent the $S$ hit, let integers $13-17$ represent $D$ .

Now let integers $18-19$ represent $T$ hit and let $20$ represent $H$ it.

Record the frequency of observed outcomes. The frequency of observed outcomes. The frequency of outcomes will vary between sets of $20$ integers.

One such set of spins can be recorded in a frequency table as follows:

Outcome	Frequency
$S$	$14$
$D$	$3$
$T$	$2$
$H$	$1$
Total	$20$

Now, divide each frequency in the frequency table to get the probabilities for each outcome.

Outcome	Frequency	Probability
$S$	$14$	$\frac{14}{20}=0.70$
$D$	$3$	$\frac{3}{20}=0.15$
$T$	$2$	$\frac{2}{20}=0.10$
$H$	$1$	$\frac{1}{20}=0.05$
Total	$20$	$\frac{20}{20}=1$

Make a probability histogram by charting probability on the vertical axis and outcomes on the horizontal axis.

  

Therefore, based on the simulation, the probability that a baseball player hits an single is $70\%$ , for double is $15\%$ , for triple is $10\%$ , and for an home run is $5\%$ .