Question

Consider 105 independent observations. The probability of event A in a particular experiment is 0.4. Choose the appropriate formula to calculate the probability that event A occurs exactly 42 times.

a. Binomial Probability Formula
b. Poisson Probability Formula
c. Normal Distribution Probability Formula
d. Geometric Probability Formula

Answer 1

To calculate the probability that event A occurs exactly 42 times out of 105 independent observations, we can use the binomial probability formula.

Step-by-step explanation:

To calculate the probability that event A occurs exactly 42 times out of 105 independent observations, we can use the binomial probability formula.

The binomial probability formula is given by P(X = k) = (n choose k) * (p^k) * (q^(n-k)), where:

• P(X = k) is the probability of getting exactly k successes
• n is the total number of observations
• p is the probability of success for each observation
• q is the probability of failure for each observation, which is equal to 1 - p
• (n choose k) is the binomial coefficient, calculated as n! / (k! * (n-k)!)

Plugging in the values from the question, we have:

P(X = 42) = (105 choose 42) * (0.4^42) * (0.6^(105-42))

Using a calculator or software, we can calculate this probability.