0.9^18 -

0.918=(0.99)20.9 to the 18th power equals open paren 0.9 to the nineth power close paren squared First, calculate 0.990.9 to the nineth power

First, ( 0.1853020188851841 \times 0.8 = 0.14824161510814728 ) Then, ( 0.1853020188851841 \times 0.01 = 0.001853020188851841 ) Add them: ( 0.14824161510814728 + 0.001853020188851841 ) Sum: ( 0.15009463529699912 ) 0.9^18

So:

Probability of failure = (1 - 0.9)^18 = 0.1^18 ≈ 0 0.9^18

In the world of mathematics, simple numbers often hide profound truths. At first glance, the expression looks like a straightforward arithmetic problem. It involves a number very close to one, raised to a modest power. 0.9^18

0.9^18 ≈ 0.1501