Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Exercise 11.4.3: Detecting a biased coin. About A gambler has a coin which is either fair (equal probability heads or tails) or is biased with a probability of heads equal to 0.3. Without knowing which coin he is using, you ask him to flip the coin 10 times. If the number of heads is at least 4, you conclude that the coin is fair. If the number of heads is less than 4, you conclude that the coin is biased. (a) What is the probability you reach an incorrect conclusion if the coin is fair

Sagot :

fichoh

Answer:

0.17189

0.3504

Step-by-step explanation:

For a fair coin ; p = 0.5

1 - p = 0.5

P(x < 4) = p(x = 0) + p(x =1) + p(x = 2) + p(x = 3)

Recall:

P(x =x) = nCx * p^x * (1 - p)^(n - x)

Using a calculator to save time:

P(x <4) = 0.00098 + 0.00977 + 0.04395 + 0.11719

P(x < 4) = 0.17189

For a unfair coin :

p = 0.3 ; 1 - p = 1 - 0. 3 = 0.7

P(x ≥ 4) = p(x=4)+p(x =5)+p(x=6)+p(x=7)+p(x=8)+p(x=9) +P(x=10)

Recall:

P(x =x) = nCx * p^x * (1 - p)^(n - x)

Using a calculator to save time:

P(x ≥4) = 0.3504

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.