Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. If the coin is assumed fair, then, for n = 2, what are the probabilities associated with the values that X can take on?
Coin tossing is a classic example of a random experiment with two possible outcomes: heads or tails. The difference between the number of heads and tails obtained in a coin tossing experiment is referred to as X. When a fair coin is tossed, the probabilities associated with the values that X can take on are dependent on the number of tosses, n.
For n = 2, X can take on the values of -2, -1, 0, 1, or 2. The probabilities associated with each of these values are:
P(X = -2) = 0, since it is impossible to have 2 tails and 0 heads in a 2 coin toss.
P(X = -1) = 1/4, since there is only 1 way to have 1 tail and 1 head in a 2 coin toss.
P(X = 0) = 1/2, since there is only 1 way to have 2 heads or 2 tails in a 2 coin toss.
P(X = 1) = 1/4, since there is only 1 way to have 2 heads and 0 tails in a 2 coin toss.
P(X = 2) = 0, since it is impossible to have 2 heads and 0 tails in a 2 coin toss.
It is important to note that these probabilities are based on the assumption of a fair coin, where the probability of getting heads or tails in each toss is equal to 1/2. In a fair coin experiment, the sum of all probabilities will always add up to 1.
Understanding the probabilities associated with X in a coin tossing experiment is crucial in making predictions and decisions in various fields such as mathematics, statistics, and gambling. By understanding the values that X can take on and the probabilities associated with them, we can gain a deeper understanding of the randomness and fairness of a coin tossing experiment.
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