 ## What is the probability that Dave will win?   There are 20 cards that will be inbetween a 5 and a Jack, out of 50 possible cards left in the deck. Therefore,
 P(a card between 5 and Jack) = # of cards between 5 and Jack = 20 = 2 = .40 # of cards that may be dealt 50 5

What does .40 mean? Converting it to a percentage, .40 = 40%. Therefore, Dave has a 40% chance of winning the game; since 40% is less than 50%, he will win this scenario less than half the time. Jamal plays the "between" game with Pierre, and deals him the two cards below:   What is the probability that Pierre will win?

It should not be shocking that the probability of Pierre winning is 0: there are not any cards that are between 3 and 4! Using the formula, we see that...
 P(a card between 3 and 4) = 0 = 0 50

Here we note an important property of the probability of an event. For any event (let's call it E) , the probability of E, or P(E) :

0 ˛ĘP(E) ˛Ę1

In other words, the probability of an event lies between 0 and 1 inclusive.
• When P(E) = 0, it signifies that the event E cannot occur.
• When P(E) = 1, it signifies that the event E always occurs.

Can you ever get a probability of 1 in the "between" game?

## Mutually Exclusive Events In probability, it is important to know whether or not it is possible for two events to occur at the same time. For instance, if a person selects one card from a deck of 52 cards, he or she may never pick both a spade and a club at the same time. Therefore, we call these events mutually exclusive. If one has two events (call them A and B), they are mutually exclusive if...

P(A and B) = 0

In words, event A and event B are mutually exclusive if the probability of A and B happening at the same time is zero (impossible).

Knowing when events are mutually exclusive helps a person when he or she must figure out probabilities involving the word "or." Pick a card from a standard deck. What is the probability that it is either a Queen or a 7? To find P(Queen or 7), we must find the number of ways that a Queen or a 7 occur in a deck of cards.    There are four Queens and four 7's, so there are 8 cards out of a total of 52 that may be selected. Thus P(Queen or 7) = 8 / 52.    Now compute P(Queen) + P(7). What do you notice?

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