Question Determine if flipping a coin twice are independent or dependent events. for independent events, for dependent events.
Studdy Solution
STEP 1
Assumptions1. We have a fair coin, which means the probability of getting a head (H) or a tail () is the same and is1/. . The two events are flipping the coin for the first time and flipping it for the second time.
STEP 2
Two events are said to be independent if the occurrence of one event does not affect the occurrence of the other event. In other words, the probability of the occurrence of both events is the product of their individual probabilities.
STEP 3
Let's denote the first flip as Event A and the second flip as Event B. According to the definition of independent events, if Events A and B are independent, then the probability of both events occurring is the product of their individual probabilities.
STEP 4
In our case, the probability of getting a head or a tail in each flip is1/2. Therefore, the probability of both events (flipping the coin for the first time and flipping it for the second time) is
STEP 5
On the other hand, the probability of getting a head or a tail in each flip is not affected by the result of the other flip. This means that the probability of Event A does not change whether Event B has occurred or not, and vice versa. Therefore, the two events are independent.
The two events described (flipping a coin and then flipping it again) are independent.
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