Emily surmises that the probability that she will pass math or chemistry is .95, the probability of her passing math is .7, and the probability of passing both is .55. Find her estimate of the probability of passing chemistry?
how about making a Venn diagram using 2 intersecting circles.
Place .55 in the intersection of the two.
Prob of passing math is .7 , but you already have put .55 in the math circle, that leaves .15 to go in the non-overlapping part of math
label the non-overlapping part of chemistry as x
then
x = .55 + .15 = .95
x = .25
so prob of passing chemistry is .55 + .25 = .8
To find Emily's estimate of the probability of passing chemistry, we can use the formula for finding the probability of the union of two events (A or B) when the probability of their intersection (A and B) is known.
Let's assume that:
P(A) represents the probability of passing math
P(B) represents the probability of passing chemistry
P(A and B) represents the probability of passing both math and chemistry
According to the question:
P(A or B) = 0.95 (the probability of passing math or chemistry)
P(A) = 0.7 (the probability of passing math)
P(A and B) = 0.55 (the probability of passing both math and chemistry)
The formula to find P(A or B) when P(A) and P(A and B) are given is:
P(A or B) = P(A) + P(B) - P(A and B)
Substituting the given values into the formula, we have:
0.95 = 0.7 + P(B) - 0.55
Now, rearrange the equation to solve for P(B):
0.95 - 0.7 + 0.55 = P(B)
0.8 = P(B)
According to Emily's estimate, the probability of passing chemistry is 0.8, or 80%.