There are three coins in a box: one double-headed, one double-tailed and one fai
ID: 3299757 • Letter: T
Question
There are three coins in a box: one double-headed, one double-tailed and one fair coin. a) I close my eyes, pick a coin from the box at random and toss it. What is the probability that the coin lands heads? b) I open my eyes and see that the coin indeed landed heads. What is the probability that it is the double-headed coin? c) I close my eyes and toss the same coin again. What is the probability that the coin lands heads? d) I open my eyes and see that the coin indeed landed heads. What is the probability that it is the double-headed coin? e) I throw the coin away, close my eyes, pick another coin from the box at random and toss it. What is the probability that the coin lands heads?Explanation / Answer
3 Coins : Double Headed , Double Tailed and Fair coin
Therefore Heads Tails
3 3
a) P ( coin lands heads when eyes are closed ) = Number of heads / Total number of sides = 3 / 6 = 0.5 .
b) P ( tossed coin in (a) is double headed ) = Number of double headed coins / Total number of coins = 1 / 3 = 0.33
c) P ( coins lands heads if it is double head ) = 0.33 / 0.5 ( from a & b ) = 0.66
d) P ( tossed coin in (a) is double headed ) = Number of double headed coins / Total number of coins = 1 / 3 = 0.33
e) The coin is thrown away , another coin is picked up .
P ( another coin which is picked up is heads )
= ( coin picked up / Remaining coins ) - P ( tossed coin is double headed)
= 1 / 2 - 0.33
= 0.5 - 0.33
= 0.17
=
Double Headed Coin Double Tailed Coin Fair Coin Head Head Tail Tail Head Tail 1 1 1 1 1 1