In the single roll of a dice, rolling a 2 is mutually exclusive of rolling a 4. When a question asks for the probability of event A "or" event B, the probability is the sum of each event.

First, find the probability of each individual event.

Because the problem asks for a 2 OR a 4, add the indivual probabilities together.

In the draw of a marble, picking a red is mutually exclusive of picking a green marble. When a question asks for the probability of event A "or" event B, the probability is the sum of each event.

First, find the probability of each event occuring.

Because the problem asks for the probability of either red OR green, we add the two probabilities.

In a single draw of a card, drawing a heart is mutually exclusive of drawing a spade, so we can use the addition rule to find the probability of a heart of a spade.

First, you must find the probability of each seperate event.

To find the probability of a heart or a spade, just add the probability of each event occuring.

This problem asks for the probability of one event or another, so we will be using the addition rule. Because the event drawing a heart is not mutually exclusive from the event drawing a Jack, we must subtract the probability of getting both. Otherwise, we will double-count the Jack of Hearts.

First, find the probability of each event occuring

Now, find the probability of drawing both a Jack and a Heart. There is one card that is both.

Now, solve the equation.

You must use the addition rule of probability which is the probability of either of two dependent events happening is the sum of the probabilities of each dependent event minus the probabilty of both happening (this eliminates double counting possible out comes).  The probabilty of getting an ace is  and the probability of getting a spade is .  The probability of getting an ace of spades is .  The final answer would then be = . 

Billy plays baseball 40%+football 30% gets 70%.

But he plays both 15% so:  

%

2 ways: 1st, sum of , since  anything above 1 represents the overlap, or 

2nd: since , the portion of the data in B and not A () is  (think venn diagram), and thus the portion of  included in A is 

Recall that when two variables are independent,

To find the probability of outcomes for two separate events, multiply the probability of the two outcomes.  Here, the two events are independent (the second event is not affected by the result of the first) and the probability is the same for both events.

The probability of the second event depends on the outcome of the first event.  Since a pen was set aside as a result of the first event, there is a slightly lower probability of a pen being selected the second time. Six pens and one pencil remain.  The probability of selecting a pen is: