Consider representing attempts of a kicker by generating random numbers. Remember to repeat the simulation several times.
See solution.
Practice makes perfect
We are told that a kicker of the local football team has made 16 out of 20 field goal attempts from less than 30 yards this season.
16/20 = 80 %
This means that the experimental probability of making his next field goal kick is 80 %.
We want to find the average number of field goals the kicker will score if he has three attempts. To do so, we will simulate the attempts by generating random numbers. Since the probability is 80 %, one out of five numbers will represent a failed attempt.
Successful Attempt:& 1, 2, 3, 4
Failed Attempt:& 0
Now we will generate numbers between 0 and 4 three times. To obtain more relevant results, we will repeat the simulation 25 times.
ccccc
222 & 024 & 34 0 & 3 04 & 4 04
233 & 044 & 444 & 443 & 2 02
2 04 & 434 & 011 & 3 01 & 322
33 0 & 32 0 & 421 & 2 04 & 132
041 & 042 & 013 & 024 & 3 00
Keep in mind that these are just several possible outcomes we can obtain to find the average number of scored field goals. Let's now calculate the number of successful attempts in each outcome.
ccccc
3 & 2 & 2 & 2 & 2
3 & 2 & 3 & 3 & 2
2 & 3 & 2 & 2 & 3
2 & 2 & 3 & 2 & 3
2 & 2 & 2 & 2 & 1
Finally, we will find the average number of field goals the kicker will make. To do so, we will divide the sum of the numbers, 57, by the number of trials. Recall that we performed 25 simulations in total.
Average Number of Field Goals [0.5em]
57/25 ≈ 2.28
Therefore, on average the kicker scores about 2.28 field goals out of three attempts.
