Question

Перед началом футбольного матча судья бросает монетку, чтобы определить, какая из команд начнёт игру с мячом. Команда «Сапфир» играет три матча с разными командами. Найдите вероятность того, что в этих играх «Сапфир» выиграет жребий ровно два раза

Answer 1

Потому что ровно 1 раз они проиграли мы эту тему с репетитором проходили

Answer 2

Calculating the Probability of "Sapphire" Winning the Coin Toss Exactly Twice

To calculate the probability of "Sapphire" winning the coin toss exactly twice in three matches, we can use the binomial probability formula. The formula for the binomial probability is:

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

Where: - n = total number of trials (in this case, 3 matches) - k = number of successful trials (in this case, winning the coin toss) - p = probability of success on an individual trial (in this case, winning the coin toss)

Applying the Formula

We can apply the formula to find the probability of "Sapphire" winning the coin toss exactly twice in three matches.

Step 1: Determine the values for n, k, and p. - n = 3 (total number of matches) - k = 2 (exactly two wins in the coin toss) - p = 0.5 (probability of winning the coin toss)

Step 2: Calculate the probability using the formula. - P(X = 2) = (3 choose 2) * (0.5^2) * (0.5^(3-2))

Calculation

- (3 choose 2) = 3 (combinations of 3 matches taken 2 at a time) - (0.5^2) = 0.25 - (0.5^(3-2)) = 0.5

P(X = 2) = 3 * 0.25 * 0.5 = 0.375

Conclusion

The probability of "Sapphire" winning the coin toss exactly twice in three matches is 0.375 or 37.5%.