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# Theoretical and Experimenatal Probability

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Probability is an important topic, and students should be able to test theoretical computations against experimental data.

Consider a deck of 52 cards with the following characteristics:
13 red cards, numbered 1 through 13
13 blue cards, numbered 1 through 13
13 green cards, numbered 1 through 13
13 black cards, numbered 1 through 13

A. Determine the theoretical and experimental probabilities:

1. Describe the steps necessary to calculate the theoretical probability of:
a. Drawing two red cards one after the other from the given deck if the cards are returned to the deck after each pick.
b. Drawing three cards with the same value one after the other from the given deck without replacing them in the deck after each pick.

2. Describe the steps necessary to calculate the experimental probabilities of:
a. Drawing two red cards one after the other from the given deck if the cards are returned to the deck after each pick.
b. Drawing three cards with the same value one after the other from the given deck without replacing them in the deck after each pick.

https://brainmass.com/math/probability/theoretical-experimenatal-probability-568371

#### Solution Preview

Hello,

For the task A1a you should:
- calculate the probability of drawing ONE red card from the deck
- using the rule of probability of independent events (http://www.mathsisfun.com/data/probability-events-independent.html) calculate the probability of drawing TWO red card from the deck, as a sequence of two single drawings.

For the task A1b you should:
- pay attention, that it doesn't matter what the first card is - the values of the second and of the third cards have to be equal to the first (the first card is needed only to say what value the ...

#### Solution Summary

The expert calculates the probabilities of sequence of independent events.

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