2-bit branch prediction accuracy
First off, I think it's important for you to specify when you do these types of problems (and clarify by asking your professor) which type of 2-bit predictor is being used, because there are 2 types.

The first type makes a transition from a weak state to the alternate weak state on failure.

The second type makes a transition from a weak state to the alternate strong state on failure.

For this problem, I am assuming it is the first type, which transitions from a weak state to the alternate weak state upon failure. That is the type shown in the picture below: 



Consider what happens in each case individually:  

WT = weakly taken
ST = strongly taken
WN = weakly not taken
SN = strongly not taken

Branch #1

Predict WT - T : 1/1

Predict ST - T : 1/1


Total : 2/2

Branch #2

Predict WT - N : 0/1

Predict WN - N : 1/1

Predict SN - N : 1/1


Total   2/3

Branch #3

Predict WT - T : 1/1

Predict ST - N : 0/1

Predict WT - T : 1/1

Predict ST - N : 0/1

Predict WT - T : 1/1


Total : 3/5

Branch #4

Predict WT - T : 1/1

Predict ST - T : 1/1

Predict ST - T : 1/1

Predict ST - N : 0/1


Total : 3/4

Branch #5

Predict WT - T : 1/1

Predict ST - T : 1/1

Predict ST - N : 0/1

Predict WT - T : 1/1

Predict ST - T : 1/1

Predict ST - T : 1/1


Total : 5/6

Total of all branches : 15/20