Question

The probability of a student missing a class is \( 0.1 \). In a total number of 10 classes, the probability that the student will not miss more than one class is _______ (rounded off to two decimal places).

Hint:

In binomial distribution problems, when calculating "at most" type probabilities, sum the probabilities from \( X = 0 \) up to the required value using the binomial formula.

Answer 1

Step 1: Recognize the binomial distribution setup. Let the number of classes missed be a binomial random variable \( X \) with parameters: \[ n = 10 \quad {(total trials)}, \quad p = 0.1 \quad {(probability of missing a class)} \] We are asked to compute: \[ P(X \leq 1) = P(X = 0) + P(X = 1) \] Step 2: Use the binomial probability formula: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] Step 3: Calculate \( P(X = 0) \) \[ P(X = 0) = \binom{10}{0} (0.1)^0 (0.9)^{10} = 1 \cdot 1 \cdot 0.3487 = 0.3487 \] Step 4: Calculate \( P(X = 1) \) \[ P(X = 1) = \binom{10}{1} (0.1)^1 (0.9)^9 = 10 \cdot 0.1 \cdot 0.3874 = 0.3874 \] Step 5: Add the probabilities \[ P(X \leq 1) = 0.3487 + 0.3874 = 0.7361 \] Step 6: Round off to two decimal places \[ \boxed{0.74} \]