SOLUTION: In a class of 50 students, 31 are democrats, 13 are business majors, and 3 of the business majors are democrats. If one student is randomly selected from the class, find the proba

Algebra ->  Probability-and-statistics -> SOLUTION: In a class of 50 students, 31 are democrats, 13 are business majors, and 3 of the business majors are democrats. If one student is randomly selected from the class, find the proba      Log On


   

Question 361410: In a class of 50 students, 31 are democrats, 13 are business majors, and 3 of the business majors are democrats. If one student is randomly selected from the class, find the probability of choosing a Democrat or business major.
Answer by neatmath(302) About Me  (Show Source):
You can put this solution on YOUR website!
There are 50 students total.

Now we need to find out how many students fit our parameters of Democrat or business major.

There are 31 Democrats, and 13 business majors. However, 3 of the business majors are ALSO Democrats.

So here are the totals we really have for Democrats and business majors:

31%2B13-3=41

Thus, the probability of choosing a Democrat or business major is just:

41%2F50 or

0.82

Therefore, P(Democrat or business major)=0.82

We could also use the formula P(A or B) = P(A) + P(B) - P(A and B) to calculate this.

This is likely how your instructor would like you to solve this problem, see below:

P(D or B)=P(D)+P(B)-P(D and B)

P(D or B)=31/50+13/50-3/50

P(D or B)=41/50=0.82 which agrees with our probability above!

I hope this helps!