The questions are all illustrations of conditional probabilities, and they can be solved using the general conditional probability formula; P(A|B) = P(A and B)/P(B)
How to determine the conditional probabilities?
The conditional probability P(A|B) is calculated using:
P(A|B) = P(A and B)/P(B)
Using the above formula, we have:
P(has at least 4 sides| not a hexagon) = 38/50
P(has at least 4 sides| not a hexagon) = 0.76
P(not a square | has less than 7 sides) = 30/45
P(not a square | has less than 7 sides) = 0.67
P(not an octagon | not a triangle) = 39/51
P(not an octagon | not a triangle) = 0.76
P(octagon | sum of interior angle measures is at least 600) = 9/25
P(octagon | sum of interior angle measures is at least 600) = 0.36
Students in Wayland high school
The conditional probability is calculated using:
P = P(perfect attendance and honor roll)/P(Honor roll)
So, we have:
P = 25%/38%
Evaluate
P = 0.66
Hence, the probability that a student has a perfect attendance, given that he made the honor roll is 0.66
Homes on the market
The conditional probability is calculated using:
P = P(Home has a pool and at least 3 bedrooms)/P(at least 3 bedrooms)
So, we have:
P = 25%/70%
Evaluate
P = 0.36
Hence, the probability that a home has a pool, given that it has at least 3 bedrooms is 0.36
Conditional probability using Venn diagram
Using the conditional probability formula in (a), we have:
P(uses Ins tag ram| does not use Sna pch at) = 45/(20 + 45)
P(uses Ins tag ram| does not use Sna pch at) = 0.69
P(does not use Ins tag ram| uses Sna pch at) = 25/(30 + 25)
P(uses Instag ram| does not use Sna pch at) = 0.45
Sports and Part-time job
Using the conditional probability formula in (a), we have:
P(plays sport| has a part-time job) = 22/68
P(plays sport| has a part-time job) = 0.32
P(has a part-time job| plays sport) = 22/40
P(has a part-time job| plays sport) = 0.55
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