1.

Toss the selected coin 10 times from a jar of 1000 coins. Out of 1000 coins, 999 coins are fair and 1 coin is double-headed, assume that you see 10 heads. Estimate the probability of getting a head in the next coin toss.

Answer»

We know that there are TWO types of coins - fair and double-headed. HENCE, there are two possible ways of choosing a coin. The first is to choose a fair coin and the second is to choose a coin having 2 heads.

P(selecting fair coin) = 999/1000 = 0.999
P(selecting double headed coin) = 1/1000 = 0.001

Using Bayes RULE,

P(selecting 10 heads in row) = P(selecting fair coin)* Getting 10 heads + P(selecting double headed coin)P(selecting 10 heads in row) = P(A)+P(B)P (A) = 0.999 * (1/2)^10 = 0.999 * (1/1024) = 0.000976P (B) = 0.001 * 1 = 0.001P( A / (A + B) ) = 0.000976 / (0.000976 + 0.001) = 0.4939P( B / (A + B)) = 0.001 / 0.001976 = 0.5061P(selecting HEAD in next toss) = P(A/A+B) * 0.5 + P(B/A+B) * 1 = 0.4939 * 0.5 + 0.5061 = 0.7531

So, the answer is 0.7531 or 75.3%.


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