If rhys is late for his finite mathenetucs class, ad the probability that he is on time is 3/4. however if he is on time, he is liale to be less concerned about punctuality for the next class and his probability being on time drops to 1/2. rhy is on time monday. find the probability that:
a) he is on time wednesday
b) he is late on thursday
To find the probabilities in this scenario, we can use the concept of conditional probability. In conditional probability, we calculate the probability of an event happening given that another event has already occurred.
Let's use the following notations:
- T: Rhys is on time
- L: Rhys is late
We are given the initial probability:
P(T) = 3/4 (probability of Rhys being on time)
We are also given that if Rhys is on time, the probability of him being on time again drops to 1/2 for the next class. Therefore, we can calculate the probability of him being late after being on time:
P(L|T) = 1 - P(T|T) = 1 - 1/2 = 1/2
Now, let's calculate the probabilities:
a) To find the probability that Rhys is on time on Wednesday, we can use the concept of independence. Since the events on Monday and Wednesday are independent, the probability of him being on time is the same.
P(T on Wednesday) = P(T) = 3/4
b) To find the probability that Rhys is late on Thursday, we need to consider the information given about Rhys being on time on Monday. Since Rhys was on time on Monday, we need to find the probability of him being late on Thursday given this information.
P(L on Thursday|T on Monday) = P(L|T) = 1/2
Therefore, the probability that Rhys is late on Thursday, given that he was on time on Monday, is 1/2.