Suppose a coin having probability 0.7 of coming up heads is tossed three times. Let X denote the number of heads that appear in the three tosses. Determine the probability mass function of X.
Tossing a coin is a classic example of a random experiment with two possible outcomes: heads or tails. In this blog post, we will explore the probability mass function of X, where X denotes the number of heads that appear in three tosses of a coin having a probability of 0.7 of coming up heads.
The possible values that X can take on are 0, 1, 2, and 3, with the following probabilities:
P(X = 0) = (0.3)^3 = 0.027
P(X = 1) = 3 * (0.3)^2 * 0.7 = 0.189
P(X = 2) = 3 * 0.3 * (0.7)^2 = 0.441
P(X = 3) = (0.7)^3 = 0.343
It is important to note that these probabilities sum up to 1, as they should in a probability mass function.
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, even when the coin is not fair.