## Dependent Probability

### Dependent probability refers to the likelihood of two events occurring in relation to each other, where the occurrence of one event affects the probability of the other event

Dependent probability refers to the likelihood of two events occurring in relation to each other, where the occurrence of one event affects the probability of the other event. In other words, the probability of the second event depends on the outcome of the first event.

To understand dependent probability, we can examine it in the context of drawing cards from a deck. Let’s say we have a standard deck of 52 playing cards, and we want to calculate the probability of drawing two red cards (without replacement) from the deck.

Initially, we have 26 red cards and 26 black cards in the deck. The probability of drawing a red card on the first draw is therefore 26/52 or 1/2 since there are 26 red cards out of 52 total cards.

Now, let’s consider the second draw. If we don’t replace the first card drawn back into the deck, the number of total cards decreases by 1 to 51. However, the number of red cards also decreases by 1, as we have removed one from the previous draw. So, for the second draw, the probability of selecting a red card depends on the outcome of the first draw.

If the first draw was a red card, then we have 25 red cards remaining out of 51 total cards. Therefore, the probability of drawing a red card on the second draw, given that the first draw was red, is 25/51.

On the other hand, if the first draw was a black card, then we have 26 red cards remaining out of 51 total cards. Hence, the probability of drawing a red card on the second draw, given that the first draw was black, is 26/51.

To calculate the dependent probability of both events occurring, we multiply the probabilities of each event happening. So, in this example, the probability of drawing two red cards is:

(1/2) * (25/51) + (1/2) * (26/51) = 25/102 + 26/102 = 51/102 = 1/2

Therefore, the dependent probability of drawing two red cards from a standard deck of cards (without replacement) is 1/2.

It is essential to note that dependent probability can also be calculated using a conditional probability formula or by considering the number of favorable outcomes divided by the number of possible outcomes in each step of the process.

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