Alice has 5 coins. Two of the coins are double-headed (both sides are heads). On

Question

Alice has 5 coins. Two of the coins are double-headed (both sides are heads). One of the coins is double-tailed (both sides are tails). The remaining two coins are normal (one side is heads and one side is tails). The normal coins are fair Alice picks one of the coins uniformly at random, closes her eyes, and she tosses the coin. What is the probability that the lower face of the coin is a heads? Alice opens her eyes and sees that the upper face of the coin is heads. What is the probability that the lower face of the coin is heads? Alice closes her eyes again, and tosses the same coin a second time. What is the probability that the lower face is heads? Alice opens her eyes and sees that the upper face of the coin is heads. What is the probability that the lower face is heads? Alice discards this coin. She picks a coin uniformly at random from the remaining coins and tosses it. What is the probabilitv that the coin shows heads? Hint: all of the questions except the first one ask you to work out a conditional probability. Carefully identify the event on which we are conditioning. What has Alice learned from the previous coin tosses?

Explanation / Answer

a)Probbility that lower is heads = 1/5* [1+1+1/2+1/2+0]=0.6

b)p( lower is heads/upper is heads) = 1/4*[1+1+0+0]=0.50

c)Probability = 1/4*[1+1+1/2+1/2]=3/4

d) Probabilty = 1/2=0.50

Please repost the repost the rest individually

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