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What is the probability that Dave will win?

5 of spades ??? Jack of hearts

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.

Example Jamal plays the "between" game with Pierre, and deals him the two cards below:

3 of clubs ??? 4 of diamonds

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

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 P(E) 1

In other words, the probability of an event lies between 0 and 1 inclusive.
Can you ever get a probability of 1 in the "between" game?

Mutually Exclusive Events

Ace of Spades

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.

In General 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."

Example Pick a card from a standard deck. What is the probability that it is either a Queen or a 7?

Solution 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.

Queen of Hearts Queen of Spades Queen of Clubs Queen of Diamonds 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.
7 of Hearts 7 of Spades 7 of Clubs 7 of Diamonds

Now compute P(Queen) + P(7). What do you notice?

Click here when you have a solution!

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