if the probability of a student taking a strength training gym class is 0.90, the probability of taking a conditioning gym classis 0.20, and the probability of taking a strength training gym class and a conditioning gym class is 0.14, what is theprobability of a student taking a strength training gym class or a conditioning gym class?

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HenriqueA428710 HenriqueA428710 · Answer 1 · 2022-10-28T17:10:36+02:00

Probability

First, we are going to name each case:

S: a student taking a strength training gym class

C: a student taking a conditioning gym class

Then,

S AND C: the probability of taking a strength training gym class AND a conditioning gym class

(since "AND" is similar as an intersection, then this could be named S∩C)

S OR C: a student taking a strength training gym class OR a conditioning gym class

(since "OR" is similar as an union, then this could be named S∪C)

We want to find the probability of S OR C, this is

P(S∪C)

We have that the probability of each is given by:

P(S) = 0.90

P(C) = 0.20

P(S∩C) = 0.14

P(S∪C) = P(S) + P(C) − P(S∩C)

Since we want to find P(S∪C) using the information we have, then we replace:

P(S∪C) = P(S) + P(C) − P(S∩C)

↓

P(S∪C) = 0.90 + 0.20 − 0.14

P(S∪C) = 1.10 − 0.14

P(S∪C) = 0.96

Now, we have found the probability of a student taking a strength training gym class OR a conditioning gym class.