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)

 

First of all you have two categories; namely sex and grade level. And you have a chance from each category to pick the desired individual. As such, these will be overlapping events.

 

You have a 21/37 probability of choosing a girl, and a 24/37 probability of choosing a freshman separately.

 

Given 2 chances fit a successful pick the pool is doubled to 74 and the possibilities added to equal 45

 

Therefore you have a 45/74 (60.8%) chance of picking a girl or a freshman.

 

2)

 

There are four each "5", "7" in a 52 card deck.

 

Therefore you have 8 chances out of 52  to pick a 5 or a 7.(15.4%)

 

Since there is only one category; namely the face of the card, these are not overlapping events.

 

Note: if the question had asked what the probability of drawing a 5 or a heart, that would be overlapping events.