The probability of my winning any game of chess I paly against my son is 0.4. if I play ten games against him.(a) What is the probability I win four?

To find the probability of winning four games out of ten, we can use the binomial probability formula. The formula is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Where:

• P(X = k) is the probability of winning exactly k games
• n is the total number of games played (in this case, 10)
• k is the number of games won (in this case, 4)
• p is the probability of winning a single game (in this case, 0.4)
• (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items

Plugging in the values, we have:

P(X = 4) = (10 choose 4) * 0.4^4 * (1-0.4)^(10-4)

Calculating the binomial coefficient:

(10 choose 4) = 10! / (4! * (10-4)!) = 210

Substituting the values:

P(X = 4) = 210 * 0.4^4 * 0.6^6

Calculating the probability:

P(X = 4) = 0.250822656

Therefore, the probability of winning four games out of ten against your son is approximately 0.2508, or 25.08%.