Question

Team A plays 3 basketball games against a team. The probability that team A will win each game is represented by

p. The polynomial representing the probability that team A wins no more than one game is:
a) 3p² − 3p+1
b) −p+3p² −3p+1
c) -p³ + 6p² −3p+1
d) −3p² + 3p−1

Answer 1

The polynomial representing the probability that team A wins no more than one game is option (d) -3p² + 3p-1.

Step-by-step explanation:

The polynomial representing the probability that team A wins no more than one game is option (d) -3p² + 3p-1.

To find the probability that team A wins no more than one game, we need to find the probability that team A wins exactly zero games and the probability that team A wins exactly one game, and add these probabilities together.

The probability that team A wins exactly zero games is (1-p) * (1-p) * (1-p) = (1-p)³.

The probability that team A wins exactly one game is (p)*(1-p)*(1-p) + (1-p)*(p)*(1-p) + (1-p)*(1-p)*(p) = 3p² - 3p(1-p) = 3p² - 3p + 1.

Adding these probabilities together, we get (1-p)³ + 3p² - 3p + 1 = -p³ + 6p² -3p + 1.