Computing Type 1 Error Rate for Coin Test

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To compute the Type I error rate for the coin test, the null hypothesis (Ho) is that the coin is fair, represented as 11/30 < p < 19/30, while the alternative hypothesis (H1) states that p is either less than 11/30 or greater than 19/30. The Type I error probability is calculated as the sum of the probabilities of observing results that fall outside the acceptance range under the null hypothesis. This involves determining P(p < 11/30) and P(p > 19/30) based on the binomial distribution for 30 tosses. The initial assessment of the approach appears to be correct.
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How would I compute the type 1 error rate of the following test:

accept that coin is fair if in 30 tosses the coin gives between 11 and 19 heads (inclusive), reject otherwise.

I guess my Ho is 11/30<p<19/30
and H1: p < 11/30 or p > 19/30

so type I prob = P(p < 11/30) + P(p > 19/30) both under Ho.
Is this correct?

thanks
 
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it should be right, i think
 

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