Question

Must be calculated in R

In twenty prey visits on carnivorous plants, if the probability of a capture in one visit is 0.2, what is the probability to have 3 to 6 captures ,
or P(3 less or equal than X less or equal than 6).

Answer 1

Solution:

Given ,

p = 0.2

n = 20

X follows Binomial(20 , 0.2)

Find P(3 less or equal than X less or equal than 6) i.e. P(3 X 6)

P(3 X 6) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

Use R software.

> dbinom(3, size=20, prob=0.2) +
+ dbinom(4, size=20, prob=0.2) +
+ dbinom(5, size=20, prob=0.2) +
+ dbinom(6, size=20, prob=0.2)

[1] 0.6472

Or we can find this using cumulative probability function.

P(3 X 6) = P(X 6) - P(X 3) + P(X = 3)

> pbinom(6, size=20, prob=0.2) - pbinom(3, size=20, prob=0.2) + dbinom(3, size=20, prob=0.2)

[1] 0.64722