I need help with this question You have either a Slcoin or a

You have either a Sl-coin or a $2-coin in your right-pants pocket, but you are unsure whichone.You grab a $2-coin from your change container - so you can buy yourself a bottle of water before your statistics class - and put it in your right-pants pocket.Prior to adding the $2-coin to you pocket, you surmise that the chance of you having a $ 1-coin is 2-times more than likely than having a $2-coin in your right-pants pocket.You arrive at school and order a bottle of water from a food service outlet on campus. The price of the bottle of water is S3.25. Since the only money you have on hand is in your right-pants pocket, you reach into your right-pants pocket and randomly pull out one of the two coins. It is a $2-coin. What is the probability that you do not have enough money to purchase the water?

Solution

If the other coin is $1, you don\'t have enough money (you have $3 total). If it is a $2, you have enough money (as you have $4 total).

As for the unknown coin,

P($1) = 2P($2)

As

P($1) + P($2) = 1

Then

2P($2) + P($2) = 1

P($2) = 1/3

P($1) = 2/3

Thus,

P(not enough money) = P(other coin is $1) = 2/3 = 0.6667 [ANSWER]