A certain country has a careless mint one coin in every 801

A certain country has a careless mint, one coin in every 801 manufectured has heads on both sides, The remaining coins have heads on one side, tails on the other as usual, a randomely selected coin made at the mint is tossed five times and falls heads each time ,what is the probability that this same coin will fall headsif it is tossed for a sixth time

Solution

There are possibilities of getting a coin

One with both sides of heads OR unbaised coin i,e heads on one side , tails on other side

Getting selected a coing of both sides of head = 1/801 with probability of getting head = 1

Getting selected a coin of both head and tail = 800/801 with probability of getting head = 0.5

Required probability = (1/801 * 1) + (800/801 * 0.5) = 1/801 + 400/801 = 401/801 = 0.500624

[ Please note that the out come of an event i.e tossing a coing is independent of outcome of previously tossed coins. ]