EITHER/OR Probabilities

Question

1) In your math class there are 16 boys and 21 girls. 9 of the boys and 15 of the girls are freshmen. If you randomly choose a student in your class, what is the probability that you'll choose a girl or a freshman? Tell whether these events are overlapping or non-overlapping.

Compute the probability that you'll choose a girl or a freshman.

??(Round to three decimal places.)

2). If you draw a card from a standard 52 card deck what is the probability that it will be a 5 or a 7? Tell whether these events are overlapping or non-overlapping.


Compute the probability.

???(Round to three decimal places.)

Answer 1

1. The probability of one event or another event happening P(A or B) is given by this formula:

 

P(A or B) = P(A) + P(B) - P(A and B).

 

Let's say that A is choose a girl, and B is choose a freshman.  There are 37 students total.  So P(A) is 21/37 and P(B) = 24/37, since 9 freshman boys + 15 freshman girls = 24.

 

P(A and B) is 15/37, since 15 of the students are both girl and freshman.  So the final answer is:

 

21/37 + 24/36 - 15/37 = 30/37 = 0.811

 

The events ARE overlapping because a student can be both a freshman and a girl.

 

2. Suppose A is pick a 5 and B is pick a 7.  There are 4 5's and 4 7's in a deck. So the probability of each event is 4/52 = 1/13.  So the probability of one or the other is P(A) + P(B) - P(A and B) = 1/13 + 1/13 - P(A and B) = 2/13 - P(A and B). 

 

But what's P(A and B)?  It's 0, because a card cannot be both a 5 and a 7.  So that means that the events are NOT overlapping, and the probability is 2/13 = 0.154.