Answer: C. [tex]0.75^4[/tex]
Step-by-step explanation:
Let x be the binomial variable that denotes the number of makes.
Since each throw is independent from the other throw , so we can say it follows Binomial distribution .
So [tex]X\sim Bin(n=4 , p=0.75)[/tex]
Binomial distribution formula: The probability of getting x success in n trials :
[tex]P(X=x)=^nC_xp^n(1-p)^{n-x}[/tex] , where p = probability of getting success in each trial.
Then, the probability of Michael Beasley making all of his next 4 free throw attempts will be :
[tex]P(X=4)=^4C_4(0.75)^4(1-0.75)^{0}[/tex]
[tex]=(1)(0.75)^4(1)\ \ [\because\ ^nC_n=1]\\\\=(0.75)^4[/tex]
Thus, the probability of Michael Beasley making all of his next 4 free throw attempts is [tex]=0.75^4[/tex]
Hence, the correct answer is C. [tex]0.75^4[/tex].
