Answer with explanation:
Probability of foul shots by Zelda
[tex]=\frac{5}{8}=0.625[/tex]
Probability of correct Shots among 8 shots
[tex]=1-\frac{5}{8}\\\\=\frac{3}{8}=0.375[/tex]
If there are 12 foul shots, we will use unitary method to find the total number of shots which must be an integral value.
5 foul shots , if there are 8 number of shots.
5 foul →8 shots
[tex]1 {\text{foul}}=\frac{8}{5}[/tex] shots
[tex]12 {\text{foul}}=\frac{96}{5}[/tex] shots
[tex]60 {\text{foul}}=96[/tex] shots
When , there are 60 foul shots, total number of shots =96
[tex]P(F)=\frac{60}{96}=0.625[/tex],where F =False shot
[tex]P(C)=1-\frac{60}{96}\\\\=\frac{36}{96}=0.375[/tex],C=Correct shot
Now, we will check the four simulation which yield ,the same probability as above.
In Option 1, when we flip a coin 12 times , total possible outcome[tex]=2^{12}=4096[/tex]
Maximum of 12 Heads can occur. And if you will find the probability of foul shots from, H=1,2,3,.....12,that is combination of (H,T)=(1,11),(2,10),....(11,1),it can not be equal to the probability of foul shots.
In Option 2,
Maximum of 10 red marbles can be drawn.
P(10 Red marbles out of 16 marbles)
[tex]=\frac{10}{16}\\\\=0.625[/tex]
=Probability of 12 foul shots
P(6 black marbles out of 16 marbles)
[tex]=\frac{6}{16}\\\\=0.375[/tex]
=Probability of 6 missed foul shots
Option 2, gives correct probability of 12 foul shots.
In Option 3, the denominator being 26, can't give probability equal to Probability of foul shots.
In option 4,
Probability(Rolling a number less than 5)
[tex]=\frac{4}{6}=0.67[/tex]
Probability(Rolling a number greater than or = 5)
[tex]=\frac{2}{6}=0.34[/tex]
In Only option 2, Probability of described Simulation, matches with foul shots as well as missed foul shot.
Option 2: Zelda can draw marbles 12 times from a bag with 10 red marbles and 6 black marbles. Drawing a red marble means a successful foul shot and drawing a black marble means a missed foul shot is correct Simulation that models the results of twelve foul shots.
