In exercise 1.d you over count the cardinality of E_4. . You need to subtract 3 from 144-3. You didnt account the scenarios {HHHHTHHHHT, HHHHTTHHHH, THHHHTHHHH}. You also forgot to add the cardinality of E_9 at the last summation you perform. In the solution for Exercise 1.1(d), the final computation uses
P(E_d) = P(E_4 ∪ E_5) + Σ_{i=6}^{10} P(E_i).
So the summation should include E_6, E_7, E_8, E_9, and E_10.
From the table in the solution, the corresponding cardinalities are
|E_6| = 28
|E_7| = 12
|E_8| = 5
|E_9| = 2
|E_10| = 1
Therefore the numerical substitution should contain
28 + 12 + 5 + 2 + 1
but the solution currently writes
28 + 12 + 5 + 1
So the term for E_9 is missing.
The affected line should be changed from
P(E_d) = 103/512 + 2^{-10}(28 + 12 + 5 + 1)
to
P(E_d) = 103/512 + 2^{-10}(28 + 12 + 5 + 2 + 1)
In exercise 1.d you over count the cardinality of E_4. . You need to subtract 3 from 144-3. You didnt account the scenarios {HHHHTHHHHT, HHHHTTHHHH, THHHHTHHHH}. You also forgot to add the cardinality of E_9 at the last summation you perform. In the solution for Exercise 1.1(d), the final computation uses
P(E_d) = P(E_4 ∪ E_5) + Σ_{i=6}^{10} P(E_i).
So the summation should include E_6, E_7, E_8, E_9, and E_10.
From the table in the solution, the corresponding cardinalities are
|E_6| = 28
|E_7| = 12
|E_8| = 5
|E_9| = 2
|E_10| = 1
Therefore the numerical substitution should contain
28 + 12 + 5 + 2 + 1
but the solution currently writes
28 + 12 + 5 + 1
So the term for E_9 is missing.
The affected line should be changed from
P(E_d) = 103/512 + 2^{-10}(28 + 12 + 5 + 1)
to
P(E_d) = 103/512 + 2^{-10}(28 + 12 + 5 + 2 + 1)