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Fan Appreciation Night, Part 1

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Since the events in this scenario are dependent, a different strategy must be applied to calculate the probability.

If Khalid’s team is given the first two draws from the grab bag, what are the chances of drawing two history questions?

Create and Analyze

One way to look at this scenario is by creating a sample space.  Each letter in the sample space represents a different category of question that may be drawn.  Let’s say the cards with the letter H are the history cards.

Thirty cards are displayed to represent the thirty questions.  Five cards are displayed for each category. A single letter on each card represents the corresponding categories: H for history; L for literature; M for mathematics; S for science; A for art, and G for geography.

The probability of drawing a history card first is 530 or 16 .

If one history card is drawn first, the sample space for the drawing of the second question would look like this:

Twenty-nine cards are displayed to represent the cards once the first history card has been drawn.  There are four history cards displayed and five cards displayed for the following categories:  literature, mathematics, science, art, and geography.

The sample space has now changed, indicating that this event is dependent and the probability of the second draw being a history card is now 429 .  If the events were independent, the sample space would not change, such as in cases where cards are replaced in the pile.

To calculate the probability of dependent events, you must multiply the probability of event A with the probability of B after A occurs.

Test and Confirm

So, the probability of drawing the first history card is 530 or 16 .  Once that card is selected, there are only 29 cards remaining and only 4 of those cards represent history questions.  The probability of drawing a second history card is 429 .  So, the probability of drawing two history questions is (16)(429)=287

Apply the Model

It would not be likely that two history questions would be drawn in a row.


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