Two chess players, a and b, are going to play 7 games. each game has three possible
outcomes: a win for a (which is a loss for b), a draw (tie), and a loss for a (which is
a win for b). a win is worth 1 point, a draw is worth 0.5 points, and a loss is worth 0
points.
(a) how many possible outcomes for the individual games are there, such that overall
player a ends up with 3 wins, 2 draws, and 2 losses?
(b) how many possible outcomes for the individual games are there, such that a ends
up with 4 points and b ends up with 3 points?
(c) now assume that they are playing a best-of-7 match, where the match will end as
soon as either player has 4 points. for example, if after 6 games the score is 4 to 2 in
favor of a, then a wins the match and they don’t play a 7th game. how many possible
outcomes for the individual games are there, such that the match lasts for 7 games and
a wins by a score of 4 to 3?

A) 210

B) 357

C) 267

Step-by-step explanation:

A) Among 7 games, we can first choose 3 wins, and then among remaining 4 games, we can choose 2.

To calculate the possibility, we will use Combination.

B) Player A can get 4 points with the following cases:

4 wins and 3 loses

3 wins, 2 draws and 2 loses

2 wins, 4 draws and 1 lose

1 win and 6 draws

Indeed, these cases matches for Player B too to get 3 points.

So again, we will use Combination to calculate the possibility.

C) Here, we need to find two possibilities after 6 games and add them, while Player A has 3 points and wins the 7th game, and Player A has 3.5 points and draws the 7th game.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

step-by-step explanation: