For a binomial distribution with parameters

Question

n = 5 , p = 0.3 . Find the probabilities of
getting :
(i) Atleast 3 successes.
(ii) Atmost 3 successes.
n = 5 , p = 0.3

Answer 1

binomial coefficients for n = 5:
1 5 10 10 5 1
p = .3
1-p = .7

P(0) = .3^0 (.7)^5 = .168
p(1) = 5 (.3)^1(.7)^4 = .360
P(2) = 10 (.3)^2(.7)^3 = .309
P(3) = 10 (.3)^3(.7)^2 = .1323
P(4) = 5 (.3)^4(.7)^1 = .028
P(5) = 1 (.3)^5(.7)^0 = .002

first answer is P(3)+P(4)+P(5)

second answer is P(0)+P(1)+P(2)+P(3)