# A total of 16 mice are sent down a maze, one by one. From previous experience, it is believed...

## Question:

A total of 16 mice are sent down a maze, one by one. From previous experience, it is believed that the probability a mouse turns right is .38. Suppose their turning pattern follows a binomial distribution. Use the PDF or the CDF command to help answer each of the following questions.

a) What is the probability that exactly 8 of the 16 mice turn right?

b) What is the probability that 8 or fewer of the 16 mice turn right?

c) What is the probability that 8 or more turn right?

d) What is the probability that more than 3, but fewer than 10 turn right?

e) What is the probability that exactly 10 turn left?

## Probability Under Binomial Distribution:

Binomial distribution is a Bernoulli experiment repeated over a given number of trials. The two possible outcomes are termed as success or failure. The number of successes are predetermined and fixed.

#### a).

Given that;

{eq}n=16\\p=0.38 {/eq}

{eq}P(x=8)=? {/eq}

Use formula or online calculator given by the link below to calculate the probability:

{eq}b(n,x,p)=^nC_xp^x(1-p)^{n-x} {/eq}

{eq}P(X=8)=0.1222 {/eq}

#### b).

{eq}\begin{align*} P(x\le 8)&=P(x=0)+P(x=1)+P(x=2)+...P(x=8)\\&=0.8924 \end{align*} {/eq}

#### c).

{eq}\begin{align*} P(x\ge 8)&=P(x=8)+P(x=9)+...P(x=16)\\&=0.2298 \end{align*} {/eq}

#### d).

{eq}\begin{align*} P(3\le x\le 10)&=P(x\le 10)-P(x\le 3)\\&=0.9875-0.0881\\&=0.8994 \end{align*} {/eq}

#### e).

Subtract 0.38 from one to get the probability of mouse turning left:

{eq}P(x=0)=0.0005 {/eq} 