Three bags each contains 5similar discs of which 3 are red and 2 are blues.
(1) if one disc is drawn at random from each bag, calculate the probability that all three discs will be the same colour.
(2)a player plays a game in which he draws one discs at random from each bags. He pays 10p to play the game. If he draws at least two blues he receives 25p, otherwise he receives nothing. Calculate his total expected loss on playing the game 100times.
2007-03-30 06:09:12 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
1) P(same color) = p(all blue) + p(all red)
p(blue) = 2/5*2/5*2/5 = 8/125
p(red) = 3/5*3/5*3/5 = 27/125
P(same color) = 8/125 + 27/125 = 35/125 = 7/25
2007-03-30 06:14:40 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Prob. of 3 red = 3/5 * 3/5 * 3/5 = 27/125
Prob. of 3 blue = 2/5 * 2/5 * 2/5 = 8/125
Prob of 3 red OR 3 blue = 27/125 + 8/125 = 35/125 = 7/25
Chance of drawing at least two blue = 2/5*2/5*1 = 4/25
Cost of playing 100 times = 10p * 100 = 1000 p
Wins 4/25 of 100 = 16 times
Winnings = 16 * 25 = 400 p
Loss = 1000 p - 400 p = 600 p
2007-03-30 13:16:00 · answer #2 · answered by ecolink 7 · 0⤊ 0⤋
(1) Three independent picks. Probability that they are all red: (3/5)^3. Probability that they are all blue: (2/5)^3. Add to get: 35/125 combined probability.
(2) Probability of drawing at least two blues... This is a binomial situation again. Thus (3 choose 3) * (2/5)^3 + (3 choose 2) * (2/5)^2*(3/5) = 8/125 + 36/125 = 44/125
Expected value of a play: 44/125 * 25p = 44/5 p = 8.8 p
On average you're giving away 1.2 p per play. Total expected loss for 100 plays: 120 p.
2007-03-30 13:15:40 · answer #3 · answered by tedfischer17 3 · 0⤊ 0⤋
1) 1/25
2)not sure on second one
2007-03-30 13:14:14 · answer #4 · answered by kristi 1 · 0⤊ 2⤋