Final answer:
The PMF (Probability Mass Function) of the number of games ending in a draw can be calculated using the binomial distribution formula. The PMF of the number of players whose games end in draws can also be calculated using the same formula.
Step-by-step explanation:
The PMF (Probability Mass Function) of the number of games ending in a draw can be calculated using the binomial distribution formula. Let's say there are n games being played, each with a probability of 0.6 of ending in a draw. The PMF of the number of games ending in a draw, k, is given by the formula:
P(k) = C(n, k) * p^k * (1-p)^(n-k)
where C(n, k) is the binomial coefficient of choosing k draws out of n games. For example, if n = 10 and k = 4, the PMF of the number of games ending in a draw is:
P(4) = C(10, 4) * 0.6^4 * 0 .4^6 = 210 * 0.129 6 * 0.046 656 = 0.986 646
To find the PMF of the number of players whose games end in draws, we can use similar logic. If there are n players, each playing one game with a probability of 0.6 of ending in a draw, the PMF of the number of players whose games end in draws, m, is given by the formula:
P(m) = C(n, m) * p^m * (1-p)^(n-m)
For example, if n = 8 and m = 3, the PMF of the number of players whose games end in draws is:
P(3) = C(8, 3) * 0.6^3 * 0.4^5 = 56 * 0.0144 * 0.0819 = 0.0661