Suppose a basketball team had a season of games with the following characteristics:Of all the games, 60% were at-home games. Denote this by H (the remaining were away games).Of all the games, 25% were wins. Denote this by W (the remaining were losses).Of all the games, 20% were at-home wins.Of the at-home games, we are interested in finding what proportion were wins. Which of the following probabilities do you need to find in order to determine the proportion of at-home games that were wins? P(H) P(W) P(H and W) P(H | W) P(W | H)

Suppose a basketball team had a season of games with the following characteristics:Of all the games, 60% were at-home games. Denote this by H (the remaining were away games).Of all the games, 25% owere wins. Denote this by W (the remaining were losses).Of all the games, 20% were at-home wins.If the team won a game, how likely is it that this was a home game? (Note: Some answers are rounded to 2 decimal places.) 0.05 0.12 0.15 0.42

Two evenly matched basketball teams (call them A and B) compete in a best-of 7 championships (the first team to win 4 games wins the championship). Once the champion has been determined, no more games are played. In each game, there is a home team and an away team. The home team wins the game with probability p ≥ 1/2, independent of all previous games. Suppose that the first three games will be held at the home of team A and the last 4 (or fewer if they are not needed) are played at the home of team B.(a) Let X be the number of games won by team A out of the first 3 games. Specify the distribution of X.(b) Find the probability that only 4 games are played.(c) Which of the two teams is more likely to win the trophy? Explain why.(d) Give an expression for the probability that team A wins the trophy, and evaluate it when p = 0.55.(e) Let Y be the number of games won by team A. Find the probability mass function for Y.(f) Evaluate the expected number of games won by team A and the expected number of games played when p = 1/2.(g) Observe (via computations or simulation) that when p = 0.55 the expected number of games won by team A is larger than that of team B, even though team B is more likely to win the trophy.

The following contingency table shows the number of games won and lost at two locations where a local baseball team had played.Wins LossesDaryl Fields 1 9Lincoln Park 5 5What is the probability that the team won a game if it played at Daryl Fields? Answer choices are rounded to the hundredths place.a.)0.50b.)0.10c.)0.85d.)0.05

In a tournament, a team has played 40 matches so far and won 30%30% of them. If they win 60%60% of the remaining matches, their overall win percentage will be 50%50%. Suppose they win 90%90% of the remaining matches, then the total number of matches won by the team in the tournament will be.

A team played 40 games in a season and won in 24 of them. In what per cent of games played did the team win?