When a biased coin is thrown 4 times, the probability of getting 4 heads is \( \frac{16}{81} \).\n\nWork out the probability of getting 4 tails when the coin is thrown 4 times. - Edexcel - GCSE Maths - Question 22 - 2019 - Paper 3

Given the probability of getting 4 heads is ( \frac{16}{81} ), we can denote this as ( P(H) = \frac{16}{81} ).\n\nAssuming the coin is biased such that the probability of getting heads (H) and tails (T) is related, we have the following relationship for probabilities:\n\n[ P(T) = 1 - P(H) = 1 - \frac{16}{81} = \frac{81 - 16}{81} = \frac{65}{81} ]\n\nNow, the probability of getting 4 tails when the coin is thrown 4 times (using the independence of events) is given by:\n[ P(T ext{ for 4 times}) = (P(T))^4 = \left( \frac{65}{81} \right)^4 ]\n\nCalculating this gives us:\n[ P(T ext{ for 4 times}) = \left( \frac{65}{81} \right)^4 = \frac{65^4}{81^4} ]\n\nThus, the probability of getting 4 tails is ( \frac{65^4}{81^4} ).