Questions: In a binomial experiment n=12 and p=21. Find P(x ≥ 1).

Transcript text: In a binomial experiment $n=12$ and $p=21$. Find $P(x \geq 1)$.

Solution

Solution Steps

Step 1: Define the Problem

We are given a binomial experiment with $ n = 12 $ trials and a probability of success $ p = 0.21 $. We need to find the probability $ P(x \geq 1) $.

Step 2: Calculate $ P(x = 0) $

The probability of exactly $ x $ successes in a binomial distribution is given by: \[ P(X = x) = \binom{n}{x} \cdot p^x \cdot q^{n-x} \] where $ q = 1 - p $.

For $ x = 0 $: \[ P(X = 0) = \binom{12}{0} \cdot (0.21)^0 \cdot (0.79)^{12} = 0.0591 \]

Step 3: Calculate $ P(x \geq 1) $

The probability $ P(x \geq 1) $ can be found using the complement rule: \[ P(x \geq 1) = 1 - P(x = 0) \]

Substituting the value of $ P(x = 0) $: \[ P(x \geq 1) = 1 - 0.0591 = 0.9409 \]

Final Answer

The probability $ P(x \geq 1) $ is: \[ \boxed{0.9409} \]

The correct answer is $ 0.9409 $.

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