Question

A binomial experiment has the given number of trials n and the given success probability p. n=13,p=0.2

(a) Determine the probability P (Fewer than 2), Round the answer to at least four decimal places. P( Fewer than 2)=

Answer 1

To determine the probability of fewer than 2 successes in a binomial experiment with 13 trials and a success probability of 0.2, we sum the probabilities for 0 and 1 success calculated using the binomial formula, rounding the result to at least four decimal places.

Step-by-step explanation:

The question is asking to calculate the probability of getting fewer than 2 successes in a binomial experiment with 13 trials and a success probability of 0.2. To find P(Fewer than 2), we need to calculate P(0 successes) + P(1 success). This is done using the binomial probability formula:

P(X = x) = (n choose x) * p^x * (1-p)^(n-x)

where n is the number of trials, p is the probability of success, and x is the number of successes. For this specific problem:

• P(0 successes) = (13 choose 0) * (0.2)^0 * (0.8)^13
• P(1 success) = (13 choose 1) * (0.2)^1 * (0.8)^12

After calculating these probabilities and summing them, we get the probability of fewer than 2 successes in 13 trials with a success probability of 0.2. Make sure to round the final result to at least four decimal places as instructed.

Answer 2

To find the probability P(Fewer than 2), calculate the probability of getting 0 or 1 success in 13 trials. Use the formula P(X) = C(n, X) * pˣ * q⁽ⁿ⁻ˣ⁾ and dd the probabilities of both cases.

Step-by-step explanation:

To find the probability P(Fewer than 2), we need to calculate the probability of getting 0 or 1 success in 13 trials. The formula to calculate the probability of X successes in a binomial experiment is: P(X) = C(n, X) * pˣ* q⁽ⁿ⁻ˣ⁾, where C(n, X) represents the number of combinations of n items taken X at a time. For P(Fewer than 2), we need to calculate P(X=0) + P(X=1).

So, P(X=0) = C(13, 0) * 0.2⁰ * 0.8¹³ = 1 * 1 * 0.1696 = 0.1696

P(X=1) = C(13, 1) * 0.2^1 * 0.8¹² = 13 * 0.2 * 0.0687 = 0.1772

Therefore, P(Fewer than 2) = P(X=0) + P(X=1) = 0.1696 + 0.1772 = 0.3468 (rounded to four decimal places).