Alice has five coins in a bag: two coins are normal (i.e., fair with one face Heads and the other face Tails), two are double-headed (i.e., both sides are Heads), and the last one is double-tailed (i.e., both sides are Tails). She reaches into the bag and randomly pulls out a coin, with each coin being equally likely to be selected. Without looking at the coin she drew, she tosses it once.
1. What is the probability that the side of the coin that lands face-down is Heads?
2. The coin lands and shows Heads face-up. Given this information, what is the probability that the face-down side is also Heads?
3. Alice discards the coin used in the first round. She knows that it showed Heads face-up but does not look at the other side of the coin. She reaches again into the bag and draws out a second coin from the 4 remaining coins, with each coin equally likely to be selected. Again, without looking at this second coin, she tosses it once. Given her knowledge of the result of the first coin toss (i.e., that it landed Heads face-up), what is the probability that this second coin toss results in Heads face-up?
let N be a normal coin, and
let DH be a double - headed coin
let DT be double-tailed
H -- heads, T --- tails
for N, prob(H) = 1/2, prob(T) = 1/2
for DH, prob(H down) = 1, prob(Tdown) = 0
for DT, prob(H down) = 0, prob(Tdown) = 1
so you could draw N or DH or DT
prob(heads down) = (2/5)(1/2) + (2/5)(1) + (1/5)(0)
= 1/5 + 2/5 = 4/5
2.
the only way this could happen is if we drew the DH coin
prob(DH) = 2/5
pataka rana ug answer.. 1/5 + 2/5=4/5? sure ka ana?
a) 3/5
b) (2/5)/(3/5)=2/3