You have a box with four coins three fair coins one twoheade

You have a box with four coins, three fair coins, one two-headed coin. You randomly choose a coin from the box and flip it.
a.What is the probability that heads appears?
b.What

Solution

You have a box with four coins, three fair coins, one two-headed coin. You randomly choose a coin from the box and flip it.
a.What is the probability that heads appears?

We\'ll assume there is an equal chance (1/4) of picking any of the 4 coins.
So P(heads) = P(first coin [then you always get heads( two headed coin)]) + P(second coin and get heads) + P(third coin and get heads)+ P(fourth coin and get heads).
Whenever you pick the first coin you get heads, so P(first coin and heads) = 1/4.
P(coin2, coin3 , coin4 and heads) = (1/2)*(1/4) = 1/8.

So P(heads) = 1/4 + 1/8 + 1/8 +1/8 = 5/8.

b.What