Answer:
[tex]0 \leq P( P_B) \leq 1[/tex]
[tex]P(P_B) = 0.17[/tex]
Step-by-step explanation:
From the given question:
The probabilities are assigned using the Subjective method.
Let the probability that his roommate will choose rock be  [tex]P(R_B) = 0.28[/tex]
Let the probability that his roommate will choose scissors be [tex]P(S_B) = 0.55[/tex]
∴
[tex]P(R_B) + P(S_B) +P(P_B) = 1[/tex]
[tex]0.28+ 0.55 + P(P_B) =1[/tex]
[tex]0.83 + P(P_B) = 1[/tex]
[tex]P(P_B) = 1 - 0.83[/tex]
[tex]P(P_B) = 1 -0.83[/tex]
[tex]P(P_B) = 0.17[/tex]
So;
[tex]0 \leq P( P_B) \leq 1[/tex]
[tex]P(P_B) = 0.17[/tex]