Hello All,
I had a small question in the quant section while doing probability I can across this following example, I am not sure how did we reach the conclusion that P(A and C) < P(A)
I.e 0.23
Here is the solution in the example:
Example:
In an experiment with events A, B, and C, suppose P (A) = 0.23, P (B) = 0.40, and P(C) = 0.85.
Also suppose events A and B are mutually exclusive, and events B and C are independent. Since
A and B are mutually exclusive, P(A or B) = P(A) + P(B) = 0.23 + 0.40 = 0.63.
Since B and C are independent, P(B or G) = P(B) + P(C) -P(B)P(C) = 0.40 + 0.85 - (0.40)(0.85)
= 0.91.
P(4 or G) and P(4 and C) can’t be found from the information given. But we can find that
P(A) + P(G) = 1.08 > 1. So P(A) + P(C) can’t equal P(A or C), which like any probability
must be less than or equal to 1. This means that A and C can’t be mutually exclusive, and that P(Aand C) ≥ 0.08.
• Since An Bis a subset of 4, we can also find that P(A and C.) ≤ P (A) = 0.23.?
And Cis a subset of A U C, so P(A or C) ≥ P(C) = 0.85.
Thus, we’ve found that 0.85 ≤ P(A or C) ≤ 1 and that 0.08 ≤ P(A and G) ≤ 0.23.
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