Question

Chris wants to put six plants in a row on his windowsill. He randomly chooses each plant to be an aloe plant, a basil plant, or a violet. What is the probability that either exactly four of the plants are aloe plants or exactly five of the plants are basil plants?

Answer 1

Probability is the study of calculating the chances or likelihood of an event occurring out of the total number of events. This likelihood is always presented as part of a whole. It could be in fractions or percentages.

There are two techniques to apply to this problem. First, we use the repeated trial equation:

P = n!/r!(n-r)! * p^(n-r) * q^r

This is used to determine the probability that an event will occur exactly 'r' times out of 'n' trials. p is the probability of success, while q is the probability of failure. Together, they add up to 1. In this case, each kind of plant has 1/3 probability. So, p=1/3 and q=2/3.

Second thing to note when dealing with probability problems are 'hint words'. When you are asked to find the probability of event A 'AND' event B happening, then you multiply their probabilities. However, when you are asked to find the probability of event A 'OR' event B happening, then you add their probabilities. Hence, the solution to this problem is:

P = 6!/4!(6-4)! * (1/3)^6-4 * (2/3)^4    +    6!/5!(6-5)! * (1/3)^6-5 * (2/3)^5
P = 0.596 or 59.6%