a To use the random number generator function on a graphing calculator, push the MATH button, then scroll right to the PRB menu and choose the fifth option, randInt(.
B
b What was the longest hot streak recorded in the simulation? Did it occur more than once?
A
a See solution.
B
b See solution.
Practice makes perfect
a A hot streak happens when a basketball player makes several free throw shots in a row. We want to design a simulation to find if hot streaks are really special or if they are just a natural run to be expected by probability.
Let a 1 represent a successful free throw.
Let a 0 represents a missed free throw.
Let's use the random number generator in our graphing calculator. To do so, push the MATH button, then scroll to the PRB menu and choose the fifth option, randInt(.
After choosing this option, enter the minimum and maximum values of the set and the number of trials. In our case, we are considering only two values, 0 and 1, so the minimum value is 0 and the maximum value is 1. We are given that a typical game has 20 free throw attempts, so the number of trials is 20. Next, push ENTER.
We will repeat this simulation 25 times, simulating 25 different games. Here is a table with the example results of our simulation.
Results
10100100011001000111
11010101101110111111
00110011110001101111
00001010101010101010
11111000111110001111
01010101010101010101
10010010100101001001
00000011111100000000
11111111000000111111
01001010011100111011
00111100001111000011
10101010101010101010
01000100010001000100
11110000111100001111
00011100011100011100
11110011100011110011
10000011111100001111
01010100000101010100
00110001110011001100
10010001000100100010
00001111000011110000
11001100011000110011
10101010111100000000
01001001010010010100
00100100100100100100
Remember, here a hot streak is represented with a sequence of 1s. Let's look at the first simulated game. There were two streaks, one with a length of 2 and one with a length of 3. The length of the longest recorded streak so far is 3.
101001000 11001000 111 Longest streak:3
Let's highlight the longest streak in each game and record its length. Note that if the longest streak in a game happens two or more times, we will highlight all of them.
Results
10100100011001000 111 Longest streak:3
11010101101110 111111 Longest streak:6
001100 1111000110 1111 Longest streak:4
000 11010101010101010 Longest streak:2
11111000 111110001111 Longest streak:5
0 10 10 10 10 10 10 10 10 10 1 Longest streak:1
100100 11100101001001 Longest streak:3
000000 11111100000000 Longest streak:6
11111111000000111111 Longest streak:8
010010100 11100 111011 Longest streak:3
00 11110000 111100011 Longest streak:3
101000101010010 1110 Longest streak:3
0000010001000 1100010 Longest streak:2
11110000 11110000 1111 Longest streak:4
000100000 11100010100 Longest streak:3
101100111000 11110011 Longest streak:4
100000 11111100001111 Longest streak:6
0 1110100000101010100 Longest streak:3
0011000 1110011001100 Longest streak:3
100 1000 1000 100 1000 10 Longest streak:1
0000 11110000 11110000 Longest streak:4
11001100011000110 111 Longest streak:3
10101010 111100000000 Longest streak:4
010010010 11110010100 Longest streak:4
10100 111100101100011 Longest streak:4
b Using the results from the table, we want to decide how long a streak would have to be before we considered it unusual. Let's take a look at our simulation from Part A.
Results
10100100011001000 111 Longest streak:3
11010101101110 111111 Longest streak:6
001100 1111000110 1111 Longest streak:4
000 11010101010101010 Longest streak:2
11111000 111110001111 Longest streak:5
0 10 10 10 10 10 10 10 10 10 1 Longest streak:1
100100 11100101001001 Longest streak:3
000000 11111100000000 Longest streak:6
11111111000000111111 Longest streak:8
010010100 11100 111011 Longest streak:3
00 11110000 111100011 Longest streak:3
101000101010010 1110 Longest streak:3
0000010001000 1100010 Longest streak:2
11110000 11110000 1111 Longest streak:4
000100000 11100010100 Longest streak:3
101100111000 11110011 Longest streak:4
100000 11111100001111 Longest streak:6
0 1110100000101010100 Longest streak:3
0011000 1110011001100 Longest streak:3
100 1000 1000 100 1000 10 Longest streak:1
0000 11110000 11110000 Longest streak:4
11001100011000110 111 Longest streak:3
10101010 111100000000 Longest streak:4
010010010 11110010100 Longest streak:4
10100 111100101100011 Longest streak:4
We can see that the lengths of the simulated hot streaks vary from 1 to 8. What is more, streaks of a length of 3 and 4 are the most common. This suggests that a streak of 9 or more could be considered unusual. Well, the player was Stephen Curry, of course!
