Question

Question 4 (20 points) A box contains three coins, two fair coins and one two-headed coin. (a) You pick a coin at random and toss it. What is the probability that it lands heads up? (b) You pick a coin at random and toss it, and get heads. What is the probability that it is the two-headed coin?

Answer 1

1 F If 1 Fair coing I fair coin I cheated win (2 Headed coln) IC head Cheated coin selected. probabability of getting = x1 poobabobility of selection coin- ㅗ 3. of cheated H probability = 2/5x². fair coin selected T probability = 3 3 x 1/2 probability = 2 head = 4 x 1 + 2 x 1 / 9) How a total probability of getting 1/3 + 3 = - Auswer WIN How let b) Ei Fair win is selected. E- 2 headed coin is selected. head. A : coins tossed get Now to find 'P/E/A) =? | rusing tead Bayes theorem. PE/A) - P(E2) P (A/E2) ple) MATE) + P1 E2) P(A/E2)

3. 3. I PLEIPIA/ED & PLEJP (ACE) PLE) = PIE9) = heed from 2 headed win. P(A/E2) = probability of getting PRATE) PINE) How using bayes P/E/A) Vz 7 x 12 2 + x1 21 % +1) Pinte, )= poobobiliny q getting from fair win. 2 theorem. PIE2) PLATE) %> x 1 = Arsnee PLE/A) td