Question

A 3-person basketball team consists of a guard, a forward, and a center. (a) If a person is chosen at random from each of three different such teams, what is the probability of selecting a complete team?(b) What is the probability that all 3 players selected play the same position?

Answer 1

Answer:

(a) 0.6667 or 66.67%

(b) 0.1111 or 11.11%

Step-by-step explanation:

(a) The first pick could be a player of any of the three positions. For the second pick, 2/3 positions could still be possible in order to get a full team. For the last pick, there is only one possible position out of three to complete the team. The probability of selecting a complete team is:

$P = 1*\frac{2}{3}*\frac{1}{3} =0.2222=22.22\%$

(b) There are only three possible ways that all players selected play the same position (3 guards, 3 forwards or 3 centers) out of 27 possible teams. The probability is:

$P=\frac{3}{27}=0.1111=11.11\%$