Use the binomial expression
(
p
+
q
)
n
to calculate a binomial distribution with n = 5 and p = 0.3.
To calculate a binomial distribution with n = 5 and p = 0.3, we can use the binomial expression:
(
p
+
q
)
n
Where
p = 0.3 (probability of success)
q = 0.7 (probability of failure, which is 1-p)
n = 5 (number of trials)
We can expand this expression using the binomial theorem:
(
p
+
q
)
n
=
(0.3 + 0.7)
5
=
0.3^5 + 5(0.3^4)(0.7) + 10(0.3^3)(0.7^2) + 10(0.3^2)(0.7^3) + 5(0.3)(0.7^4) + 0.7^5
Simplifying this expression, we get:
0.000243 + 0.00243 + 0.010206 + 0.026334 + 0.041790 + 0.168070
So the binomial distribution with n = 5 and p = 0.3 is:
P(X = 0) = 0.000243
P(X = 1) = 0.00243
P(X = 2) = 0.010206
P(X = 3) = 0.026334
P(X = 4) = 0.041790
P(X = 5) = 0.168070