6 When a child completes an online exercise called a Mathlit, they might be awarded a medal. The publishers claim that the probability that a randomly chosen child who completes a Mathlit will be awarded a medal is \(\frac { 1 } { 3 }\). Asha wishes to test this claim. She decides that if she is awarded no medals while completing 10 Mathlits, she will conclude that the true probability is less than \(\frac { 1 } { 3 }\).

1. Use a binomial distribution to find the probability of a Type I error.
   The true probability of being awarded a medal is denoted by \(p\).
2. Given that the probability of a Type II error is 0.8926 , find the value of \(p\).