You have 1,000 coins, and 995 of them are fair (equal probability of heads or tails). Five of them are weighted and have a 95% probability of landing on heads. You randomly choose one of the 1,000 coins. Find the probability that it is a weighted coin, under the following scenarios. (a) You flip it 10 times and it lands on heads 9 times (b) You flip it 20 times and it lands on heads 18 times

(a) 0.001575

(b) 0.009434

Step-by-step explanation:

(a) Let the event be P(W).

P(W) = P(weighted) × P(x= no of flips)

P(x) is given by a Bernoulli distribution and is given the probability of a head or tail landing during n flips

P(x)= nCr (p)^r (q), q= 1-p

P = 95% =0.95 q= 0.05. Hence for n=10 flips, r=9

P(W)=( 5/1000) × 10C9 (0.95)^9 (0.05)¹

P(W)= 0.005 × 0.3151= 0.001575

(b) P(W) = (5/1000) × 20C18 (0.95)^18(0.05)^2

P(W) = 0.009434

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step-by-step explanation: