5 gold marbles,
25 silver marbles, and
70 red marbles.
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100 total marbles
large prize: drawing a gold marble
small prize: drawing a silver marble.
At the start of the game,
probability of winning a
large prize = positive outcoumes / total possible outcomes = 5 gold marbles / 100 total marbles = 0.05
probability of winning a small prize = positive outcomes / total possible outcomes = 25 silver marbles / 100 total marbles = 0.25.
1. Suppose that the first player draws a silver marble and
wins a small prize. What is the probability that the second player will
also win a small prize?
Answer:
numer of silver marbles / number of total marbles = (25 -1 ) / (100 - 1) = 24 / 99 ≈ 0.24
2. If a group of four plays the game
one at a time and everyone wins a small prize, which player had the
greatest probability of winning a large prize?
Answer:
First player: 0.25
Second player: 5 gold marbles / ( 100 - 1) total marbles = 5 /99 ≈ 0.0505
Third player: 5 gold marbles / (99 - 1) total marbles = 5 / 98 ≈ 0.051
Fourth player: 5 gold marbles / ( 98 - 1) total marbles = 5 / 97 ≈ 0.0515
So, the probability of winning a big prize increases as more balls different of gold marbles are extracted from the bag, and so, in this case, the fourth player has a greater chance to win a large prize.
3. How could the
game be made fair for each player? That is, how could you change the
game so that each player has an equal chance of winning a prize?
Answer: All the players would have equal chance of winning a prize if the balls were replaced in the bag after each play.
