If rhys is late for his finite mathematics class, and the probability that he is on time is 3/4. however if he is on time, he is liable 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, we need to use conditional probability. Let's take a step-by-step approach to solve this problem.
a) Probability that Rhys is on time on Wednesday:
Based on the given information, we know that Rhys being on time on Monday is independent of his punctuality on Wednesday. So, the probability that he is on time on Wednesday is simply the probability that he is on time overall, which is 3/4.
b) Probability that Rhys is late on Thursday:
To find this probability, we need to consider the conditional probabilities. We'll break it down into two cases:
Case 1: Rhys is on time on Monday and late on Thursday:
The probability that Rhys is on time on Monday is given as 3/4. Given that he is on time on Monday, the probability that he is late on Thursday is given as 1 - 1/2 = 1/2 (since the probability of being on time drops to 1/2).
Case 2: Rhys is late on Monday and late on Thursday:
The probability that Rhys is late on Monday is 1 - 3/4 = 1/4. Given that he is late on Monday, the probability that he is late on Thursday remains the same, which is 1/2.
To calculate the total probability that Rhys is late on Thursday, we sum up the probabilities from both cases:
Probability (Rhys is late on Thursday) = (Probability of Case 1) + (Probability of Case 2)
= (3/4) * (1/2) + (1/4) * (1/2)
= 3/8 + 1/8
= 4/8
= 1/2
Therefore, the probability that Rhys is late on Thursday is 1/2.