Let B ∼ Bin(20,0.2). Compute the following probabilities. I would suggest computing these with a hand calculator using the formula provided in class (you will not have R on the exams!), but you can check your answers using R if you wish.

(a) P(B=4).

(b) P(B≤1).

(c) P(B>1).

a) 0.2182

b) 0.0691

c) 0.9309

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly b successes on n repeated trials, and B can only have two outcomes.

In which is the number of different combinations of b objects from a set of n elements, given by the following formula.

And p is the probability of B happening.

In this problem we have that:

Bin(20,0.2).

This means that

(a) P(B=4).

(b) P(B≤1).

(c) P(B>1).

Either B is less than or equal to 1, or B is larger than 1. The sum of the probabilities of these events is decimal 1. So

We have that, from b),

So

A

Step-by-step explanation:

Because if you look up y=2x+2 that graph rises and if you look up y=-2x+2 it decreases