CLaudia has 4 task to do go to the market, study, clean , sport it is known
- go to the market if study
- study if she does not clean
- if she does not clean then she goes to the market
a 15%
b 12%
c 10%
d 24%
To find out the probability of Claudia performing each task, we can make use of conditional probability. Let's break down the given conditions and calculate the probabilities step by step.
1. Probability of Claudia going to the market if she studies (P(go to market | study) = 15% or 0.15)
2. Probability of Claudia studying if she does not clean (P(study | not clean) = 12% or 0.12)
3. Probability of Claudia going to the market if she does not clean (P(go to market | not clean) = 10% or 0.10)
4. Probability of Claudia not cleaning if she does not go to the market (P(not clean | not go to market) = 24% or 0.24)
Now, let's calculate the probabilities using the given information:
1. Probability of Claudia going to the market:
P(go to market) = P(go to market | study) * P(study) + P(go to market | not clean) * P(not clean)
= 0.15 * P(study) + 0.10 * P(not clean)
2. Probability of Claudia studying:
P(study) = P(study | not clean) * P(not clean)
= 0.12 * P(not clean)
3. Probability of Claudia not cleaning:
P(not clean) = P(not clean | not go to market) * (1 - P(go to market))
= 0.24 * (1 - P(go to market))
Now, we need to solve these equations simultaneously using a bit of algebra.
Substituting (2) into (1):
P(go to market) = 0.15 * (0.12 * P(not clean)) + 0.10 * P(not clean)
Simplifying the equation:
P(go to market) = 0.018 * P(not clean) + 0.10 * P(not clean)
P(go to market) = 0.118 * P(not clean)
Substituting (3) into (1):
P(go to market) = 0.15 * (0.12 * P(not clean)) + 0.10 * P(not clean)
P(go to market) = 0.018 * P(not clean) + 0.10 * P(not clean)
P(go to market) = 0.118 * P(not clean)
Now, we can solve these two equations simultaneously:
P(go to market) = 0.118 * P(not clean) ---(A)
P(go to market) = 0.118 * P(go to market) ---(B)
Let's rearrange equation (B):
P(go to market) - 0.118 * P(go to market) = 0
0.882 * P(go to market) = 0
P(go to market) = 0 / 0.882
P(go to market) = 0
Since P(go to market) = 0, we can conclude that Claudia will not be going to the market as long as the given conditions hold.
As for the probabilities of the other tasks, without further information or conditions, we cannot calculate them accurately.