Write Probability distribution of the random variable of having number of red color cards when 3 cards are drawn from a pack of 52 cards. Find the mean of the distribution
Let X be the random variable representing the number of red color cards drawn when 3 cards are drawn from a pack of 52 cards.
The possible values of X can be 0, 1, 2, or 3.
The probability distribution of X is as follows:
P(X = 0) = (26C0 * 26C3) / 52C3
P(X = 1) = (26C1 * 26C2) / 52C3
P(X = 2) = (26C2 * 26C1) / 52C3
P(X = 3) = (26C3 * 26C0) / 52C3
Calculating these probabilities:
P(X = 0) = (1 * 2600) / 22100 = 0.1171
P(X = 1) = (26 * 325) / 22100 = 0.3850
P(X = 2) = (325 * 26) / 22100 = 0.3850
P(X = 3) = (2600 * 1) / 22100 = 0.1171
Therefore, the probability distribution is:
X = 0 with probability 0.1171
X = 1 with probability 0.3850
X = 2 with probability 0.3850
X = 3 with probability 0.1171
To find the mean of the distribution, we use the formula:
mean = Σ (xi * P(xi))
mean = (0 * 0.1171) + (1 * 0.3850) + (2 * 0.3850) + (3 * 0.1171)
mean = 0 + 0.3850 + 0.7700 + 0.3513
mean = 1.5034
Therefore, the mean number of red color cards drawn when 3 cards are drawn from a pack of 52 cards is 1.5034.