Chess o.0 (1 Viewer)

[zeebobDD]

In a game of Chess between two players X and Y, both of approx. equal ability, the player with the white pieces, having the first move, has a probability of 0.5 of winning, and the probability that the player with the black pieces, for that game winning is 0.3.

i) What is the probability that the game ends in a draw?

ii) The two players X and Y play each other in a chess comp, each player having the white pieces once. In the comp. the player who wins a game scores 3 points, and a player who loses a game scores 1, and in a draw each player receives 2 points. Find the probability of these two games

a) X scores 6 points
b) X scores less than 4 points

very long question, but iv got part i) and a of part ii) im not sure about my answer for ii) can someone please post up soln's please.

 

[shamimi95]

i got 0.31..

 

[zeebobDD]

hmm i got 0.59

 

[RealiseNothing]

ii)a) For X to get 6 points, he must win both games. 50% chance he wins the first, 30% chance he wins the second. So there is a 15% chance player X gets 6 points.

ii)b) If player X has to get under 4 points, he must either get 2 or 3 points since 0 and 1 are impossible (you get 1 point for a loss, so two losses is still 2 points).

There are three cases:

He loses both games: 30% as white, 50% as black, so 15% by multiplying together.

He draws then loses: 20% as white, 50% as black, so 10%.

He loses then draws: 30% as white, 20% as black, so 6%.

Add them all together 15+10+6.

So the answer is 31%.

But when you add up all the possibilites, it doesn't add to 100%.....

 

[shamimi95]

ii)a) For X to get 6 points, he must win both games. 50% chance he wins the first, 30% chance he wins the second. So there is a 15% chance player X gets 6 points.

ii)b) If player X has to get under 4 points, he must either get 2 or 3 points since 0 and 1 are impossible (you get 1 point for a loss, so two losses is still 2 points).

There are three cases:

He loses both games: 50% as white, 70% as black, so 35% by multiplying together.

He draws then loses: 20% as white, 70% as black, so 14%.

He loses then draws: 50% as white, 20% as black, so 10%.

Add them all together 35+14+10.

So the answer is 59%.

ohh.. i presumed as there is a 20% chance of draw, there would only be a 50% chance of losing as black.

 

[RealiseNothing]

ohh.. i presumed as there is a 20% chance of draw, there would only be a 50% chance of losing as black.

I think you may be right actually.

But then when you add up all the possibilities, it doesn't add to 100% lol.

 

[shamimi95]

I think you may be right actually.

But then when you add up all the possibilities, it doesn't add to 100% lol.

i thought playing white would give you a :
50% win
30% loss
20% draw

and black being:
30% win
50% loss
20% draw

 

[zeebobDD]

the answer is defs 0.31 or 0.59 CAAAAAROOOOOOOOT HEELP!!!!

 

[RealiseNothing]

i thought playing white would give you a :
50% win
30% loss
20% draw

and black being:
30% win
50% loss
20% draw

I mean the possible outcomes of how many points X can win doesn't add to 100%.

 

[shamimi95]

it does.

if you win as white
0.5 x 0.3 = 0.15 (win win)
0.5 x 0.2 = 0.10 (win draw)
0.5 x 0.5 = 0.25 (win loss)

0.25+0.1+0.15=0.5

draw as white
0.2 x 0.3 = 0.06 (draw win)
0.2 x 0.2 = 0.04 (draw draw)
0.2 x 0.5 = 0.10 (draw loss)

0.06+0.04+0.1=0.2

loss as white
0.3 x 0.3 = 0.09 (loss win)
0.3 x 0.2 = 0.06 (loss draw)
0.3 x 0.5 = 0.15 (loss loss)

0.09+0.06+0.15=0.3

0.5+0.2+0.3 = 1