Without looking, a player chooses one marble from each bucket in the Red and Blue game. If the player gets a red and blue marble they win. Each player pays $1.00 to win and if wins gets $3.00. One bucket contains 1blue,1green,1red,1yellow. The second bucket contains 1red,1green,1yellow.
Suppose the game is played 36 times, how much money can the school expect to collect?
wll...they need 2 things to happen to win
1) a blue marble from the first bucket (1 in 4 chance)
2) a red marble from the 2nd (1 in 3 chance)
so the chance for a win is (1/4) times (1/3) or (1/12)
if the game is played 36 times, then statistically 3 poeple should win
(36 X 1/12 = 3)
now if playyed 36 times the school will collect $36
if 3 won they will loose (3X$3 = $9)
so the net sum is 36-9 or $27
Ok I get it now!!!! Thank you so much!
To calculate how much money the school can expect to collect, we need to determine the probability of winning for each player and then multiply it by the number of times the game is played.
Let's start by analyzing the possible outcomes for each bucket:
Bucket 1 (1 blue, 1 green, 1 red, 1 yellow):
- There are 4 marbles in total.
- The probability of picking a red and blue marble from this bucket is: (1/4) * (1/4) = 1/16.
Bucket 2 (1 red, 1 green, 1 yellow):
- There are 3 marbles in total.
- The probability of picking a red and blue marble from this bucket is 0 because there is no blue marble.
Now we can calculate the overall probability of winning:
- Since each player selects one marble from each bucket, the probability of winning is the product of the probabilities of winning from each bucket.
- The probability of winning from Bucket 1 is 1/16.
- The probability of winning from Bucket 2 is 0.
- Thus, the overall probability of winning is 1/16 * 0 = 0.
Since the probability of winning is 0, the school will not collect any money from this game. The expected amount collected is $0.00.