We will use the Binomial Probability formula to solve this problem
The formula is given by ⁿCₓ (p)ˣ (1-p)ⁿ⁻ˣ
Where
n = the number of trials = 30 days
x = the number of days we are trying to aim which is ≤2
p = the probability of success = 1/10 = 0.1
ⁿCₓ = [tex] \frac{n!}{(n-x)!x!} [/tex] or if you have a scientific formula, type in the value of n, then find the symbol [tex]^nC_r[/tex] on the calculator, then enter the value of x.
Since we want to find the value for P(X≤2), we need to work out separately the value of P(0), P(1), and P(2) then total the answers
P(0) = ³⁰C₀ (0.1)⁰ (1 - 0.1)³⁰⁻⁰
P(0) = ³⁰C₀ (0.1)⁰ (0.9)³⁰
P(0) = 0.0424
P(1) = ³⁰C₁ (0.1)¹ (0.9)²⁹
P(1) = 0.1413
P(2) = ³⁰C₂ (0.1)² (0.9)²⁸
P(2) = 0.228
P(X≤2) = P(0) + P(1) + P(2)
P(X≤2) = 0.0424 + 0.1413 + 0.2277
P(X≤2) = 0.4114
Probability raining 2 days at the most in June is 0.4114 = 41.14%
