Binomial Distribution Math Example 2

Solution

1. 1
   Here $n = 10$, $p = 0.25$. We need $P(X \ge 2) = 1 - P(X = 0) - P(X = 1)$.
2. 2
   $P(X = 0) = \binom{10}{0}(0.25)^0(0.75)^{10} = (0.75)^{10} \approx 0.0563$.
3. 3
   $P(X = 1) = \binom{10}{1}(0.25)^1(0.75)^9 = 10 \times 0.25 \times (0.75)^9 \approx 10 \times 0.25 \times 0.0751 \approx 0.1877$.
4. 4
   $P(X \ge 2) = 1 - 0.0563 - 0.1877 = 0.756$.