You have either a $1-coin or a $2-coin in your right-pants pocket, but you are u

Question

You have either a $1-coin or a $2-coin in your right-pants pocket, but you are unsure which one. 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 5-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 $3.2. 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

Explanation / Answer

probability of getting $2 coin =P(initially having a $1 coin and then getting $2 coin+initially having a $2 coin and then getting $2 coin) =(5/6)*(1/3)+(1/6)*(2/3) =7/18

hence probability of not having eough money

=P(initially having a $1 coin and then getting $2 coin)/P(getting $2 coin) ==(5/6)*(1/3)/(7/18) =5/7=0.7143

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