5. (20 points) Tom tosses a fair coin twice and he also rolls a single fair...

Transcribed Image Text:

5. (20 points) Tom tosses a fair coin twice and he also rolls a single fair die (with sample space {1,2, 3, 4, 5, 6}) twice. Then he calculate a number from this process in the following way. He multiply the sum of 2 numbers shown on the die by 2 numbers from the results of tossing coins, i.e. multiply by 1 if the coin shows tail or by 2 if the coin shows head.For example, if the coin show head once and tail once and he get 2, 3 from rolling die twice, then he got the final number (2 + 3) × 2 x 1 = 10. For example, if the coin show head twice and he get 1,6 from rolling die twice, then he got the final number (1+6) x 2 x 2 = 28. What is the probability that Tom get 12 as the final number from this process? 5. (20 points) Tom tosses a fair coin twice and he also rolls a single fair die (with sample space {1,2, 3, 4, 5, 6}) twice. Then he calculate a number from this process in the following way. He multiply the sum of 2 numbers shown on the die by 2 numbers from the results of tossing coins, i.e. multiply by 1 if the coin shows tail or by 2 if the coin shows head.For example, if the coin show head once and tail once and he get 2, 3 from rolling die twice, then he got the final number (2 + 3) × 2 x 1 = 10. For example, if the coin show head twice and he get 1,6 from rolling die twice, then he got the final number (1+6) x 2 x 2 = 28. What is the probability that Tom get 12 as the final number from this process?