Question

Trix are for Kids": The Trix Rabbit conducted a survey. Out of 3,000 kids, 78% of them like Trix. Find the probability that at least 900 of them like Trix.

Answer 1

To find the probability that at least 900 of the 3,000 kids like Trix, calculate the probability for each scenario from 900 to 3,000 and then add up all these probabilities using the binomial distribution.

Step-by-step explanation:

To find the probability that at least 900 of the 3,000 kids like Trix, we need to determine the probability of different scenarios where the number of kids who like Trix is greater than or equal to 900. Since each kid has a 78% chance of liking Trix, we can use the binomial distribution to calculate these probabilities.

1. The probability that exactly 900 kids like Trix can be calculated using the formula P(X = k) = (nCk) * p^k * (1-p)^(n-k), where n is the total number of kids, k is the number of kids who like Trix, and p is the probability that a kid likes Trix. Plug in the values: P(X = 900) = (3000C900) * 0.78^900 * (1-0.78)^(3000-900)
2. Calculate the probability for each scenario (900, 901, 902, ..., 3000)
3. Add up all these probabilities to find the probability that at least 900 kids like Trix.