Mrs. Brown decides to change her experiment. This time, she plans to roll the die until she gets a three. She wants to know the probability of getting her first three on her 5th roll.
Explain why this is an example of a geometric experiment
Define the variables for finding the geometric probability distribution.
P = probability of success (rolling a three) =
n = number of events until success =
that is the same as
P(~3,~3,~3,~3,3) = (5/6)^4 * (1/6)^1
Mrs. Brown decides to change her experiment. This time, she plans to roll the die until she gets a three. She wants to know the probability of getting her first three on her 5th roll.
Explain why this is an example of a geometric experiment
This situation is an example of a geometric experiment because it involves repeated trials, with each trial having two possible outcomes: either a success (rolling a three) or a failure (rolling any other number). In a geometric experiment, we keep repeating the trials until we achieve the first success.
To define the variables for finding the geometric probability distribution, we have:
P = probability of success (rolling a three) = 1/6, since there is only one favorable outcome (rolling a three) out of the six possible outcomes when rolling a standard six-sided die.
n = number of events until success = 5, as specified in the question, indicating that Mrs. Brown rolls the die five times before getting her first three.
By using these variables, we can calculate the geometric probability of rolling a three on the fifth roll.