Question

6 X Yos have seven coins in youe pocket coins Ceech with probsbility of "heads0.5o Pour two-heaed cons (each with probslity of heade1.0 Suppose you randomily select a coin and g it Find the probablity of lipping "bead Now suppose that you do, in fact, Bip "heads" Givea hat information, find the probabibty that the coin you aipped was: b. A fair con? sA two-headed coin? d. Now suppose that when you flip it, the coin comes up "tails". Given that information, what is the probability that you picked the fair coin? Extra Credit After completing the above experiment, you place the coin back in your pocket (so that your pocket again holds the seven coins). Next, you reach into your pocket and select two coins. What is the probability that you select two fair coins? e

Answer 1

3 fair coins, 4 2-headed coins
probability of getting a fair coin = P(F) = 3/(3+4) = 3/7
probability of getting a two headed coin P(UF) = 4/7
(a)
probability of getting head P(H)
= P(F).P(H|F) + P(UF).P(H|UF)
= 3/7.1/2 + 4/7.1
= 11/14
(b)
P(F|H) = P(F).P(H|F)/P(H)
= 3/7.1/2.14/11
= 3/11
(c)
P(UF|H) = P(UF).P(H|UF)/P(H)
= 4/7.1.14/11
= 8/11
(d)
P(F|T) = 1 coz two headed coin doesnt have tail
(e)
possible cases are -
2 fair coins
one fair one two headed coin
2 two headed coins
So probability will be 1/3