Question

A bag contains marbles, two of which are blue. Hayley plays a game in which she randomly draws marbles out of the bag, one after another, without replacement. The game ends when Hayley draws a blue marble. Find the probability, in terms of , that the game will end on her first draw. 9b. [3 marks] Find the probability, in terms of , that the game will end on her second draw. 9c. [2 marks] Let = 5. Find the probability that the game will end on her third draw. 9d. [2 marks] fourth draw. 9e. [7 marks] Hayley plays the game when = 5. She pays $20 to play and can earn money back depending on the number of draws it takes to obtain a blue marble. She earns no money back if she obtains a blue marble on her first draw. Let M be the amount of money that she earns back playing the game. This information is shown in the following table. Find the value of so that this is a fair game.

Answer 1

Answer:

A)2/y

B)2/(y-1)

C)2/(y-2)

D)2/(y-3)

Step-by-step explanation:

Based on the information available :

Let the total number of marbles = y

Number of blue marbles = 2

Game ends when Hayley draws a blue marble.

NB: Marble is drawn without replacement

A.) P(game ends on first draw) = (number of blue marbles) / total number of marbles

P(game ends on first draw) = 2/y

B.) P(game ends on second draw) :

If game doesn't end on first draw, then no blue marble was drawn on the first pick

P(game ends on second draw) = 2/(y-1)

C.)P(game ends on third draw) = 2 / (y-2)

D.)P(game ends on fourth draw) = 2/(y-3)

There isn't enough information to solve the remaining problems