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
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