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I need some help on this problem please. Thanks List Next Problem You have eithe

ID: 2921750 • Letter: I

Question


I need some help on this problem please. Thanks

List Next Problem You have either a $1-coin or a s2-coin in your right-pants pocket, but you are unsure which one. You grab a $2-coi Prior to adding the $2-coin n 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. to you pocket, you surmise that the chance of you having a $1-coin is 4-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 $3.12. 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? Enter your answer to four decimal places. Preview My Answers Submit Answers

Explanation / Answer

The probability of having $1 earlier is 4 times higher than probability of having $2

so Pr($1) = 4 Pr($2)

that also means Pr($1) = 0.8

and Pr($2) = 0.2

Now, that was the prior distribution.

Now he pick a $2 coin in his pocket.

so there may be 2 $ 2 coin in his pocket or 1 $2 coin in pocket.

now he draws a coin, and it was a $2 coin.

so Pr( Second coin is $2 l First coin is $2) =?

so Pr(First Coin drawn is $2 ) = Pr(The coin in pocket was $1 coin) * Pr( the later picked coin is $2 coin) + Pr( The coin in pocket was $2 coin) * Pr(The later picked coin is $2 coin)

= 0.8 * 0.5 + 0.2 * 1 = 0.6

so there was 0.6 probability that first drawn coin is $2 coin.

Now we have to find that the other coin is $2. Probability of that happening is

Pr( Second Coin is $2) = Pr (Second coin is in pocket is $1) * Pr(Second coin is drawn from pocket is $2) + Pr( second coin in pocket is $2) * Pr ( Secon drawn coin is $2)

= 0.8 * 0 + 0.2 * 1 = 0.2

so Pr( Second coin is $2 l First coin is $2) = 0.2/0.6 = 1/3

so probability that i will not have enough money to buy water = 1 - 1/3 = 2/3 = 0.6667