Let π
1,π
2,π
5 be a random sample from a π΅ππ(1, π) distribution, where πβ(0,1) is an unknown parameter. For testing the null hypothesis π»
0 βΆ πβ€ 0.5 against π»
1 :π>0.5, consider the two tests π1 and π2 defined as:
π
1: Reject π»
0 if, and only if,
i=1β5β π
π=5.
π
2: Reject π»
0 if, and only if,
i=1β5β X
iβ₯3.
Let π½
π be the probability of making Type-II error, at π=
32β, when the test π
π , π=1,2 , is used. Then, the value of π½
1+π½
2 equals ________(round off to two decimal places)