Answer:
0.0286 = 2.86% probability that today is Monday.
Explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Dressed correctly
Event B: Monday
Probability of being dressed correctly:
100% = 1 out of 4/7(mom dresses).
(0.5)^3 = 0.125 out of 3/7(toddler dresses himself). So
![P(A) = 0.125(3)/(7) + (4)/(7) = (0.125*3 + 4)/(7) = (4.375)/(7) = 0.625](https://img.qammunity.org/qa-images/2022/formulas/mathematics/college/w4wwhbbl1gt0orsbwj5a9b.png)
Probability of being dressed correctly and being Monday:
The toddler dresses himself on Monday, so (0.5)^3 = 0.125 probability of him being dressed correctly, 1/7 probability of being Monday, so:
![P(A \cap B) = 0.125(1)/(7) = 0.0179](https://img.qammunity.org/qa-images/2022/formulas/mathematics/college/4d1vopbiuhnqjr1awbia33.png)
What is the probability that today is Monday?
![P(B|A) = (P(A \cap B))/(P(A)) = (0.0179)/(0.625) = 0.0286](https://img.qammunity.org/qa-images/2022/formulas/mathematics/college/hputzlwouo8sxd2p0dsnws.png)
0.0286 = 2.86% probability that today is Monday.