Question

Naruto is taking an important multiple choice ninja exam that is 5 questions long. Each question has 3 possible answers. What is the probability that Naruto will get 4 or more correct answers just by guessing? (If X is the (random variable giving the) number of correct answers Naruto gets while guessing, then convince yourself that X = Bin(n, p) for a good choice of n and a good choice of p.)

Answer 1

Answer:

0.37

Step-by-step explanation:

Let n=5 and r=3.

Probability of answering correctly =p

Probability of answering incorrectly =q.

$p=\frac{3}{5}[\tex] and [tex]q=1-\frac{3}{5}=\frac{2}{5}[\tex]Now the formula for Binomial probability is giving as B(n,p)=[tex] P(X\geq x)=\frac{n!}{(n-r)!r!}p^{r}q^{n-r}[\tex]Probability that Naruto will get 4 or more correct answers just by guessingimplies [tex]=P(X[tex]\geq 4=P(4)+P(5)=\frac{5!}{(5-4)!4!}(\frac{3}{5})^{4}(\frac{2}{5})^{5-4}+\frac{5!}{(5-5)!5!}(\frac{3}{5})^{5}(\frac{2}{5})^{5-5}$

[tex]=\frac{5!}{4!}\frac{3}{5})^{4}(\frac{2}{5})+\frac{5!}{5!}{3}{5})^{4}(\frac{2}{5})^{0}=5\frac{81}{625}\frac{2}{5}+(\frac{3}{5})^{5}[\tex]

[tex] =5\times \frac{162}{3125}+\frac{243}{3125}=\frac{810}{3125}+\frac{243}{3125}=\frac{1053}{3125}=0.33696\approx 0.37 [\tex]

Hope its clear enough.

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Answer 2

Answer:

0 -__-

Step-by-step explanation:

we all know naruto would get 0