The marketing department of a company would like to introduce 12 monthly special products in the coming 12 months. If these monthly special products are selected randomly from 24 products, find the probability that two specific products are the monthly special products in two consecutive months.
To find the probability that two specific products are the monthly special products in two consecutive months, we need to calculate the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
Since there are 24 products to choose from each month, the total number of outcomes for each month will be 24.
Total number of favorable outcomes:
Let's assume the two specific products that need to be selected consecutively are A and B.
First, we need to select A as the monthly special product. The probability of selecting A is 1 out of 24 (since there are 24 products to choose from).
Then, in the next month, we need to select B as the monthly special product. The probability of selecting B is now 1 out of 23 (since we have already selected one product in the previous month).
Therefore, the total number of favorable outcomes is 1/24 * 1/23 = 1/552.
To calculate the probability, we divide the number of favorable outcomes by the total number of outcomes:
Probability = Number of favorable outcomes / Total number of outcomes = (1/552)/(24/24) = 1/552.
So, the probability that two specific products are the monthly special products in two consecutive months is 1/552.