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

7

step-by-step explanation:

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right