Answer:
The probability is [tex]P(S | (O ,U)' ) = 0.05[/tex]
Step-by-step explanation:
From the question we are told that
The probability of each company to be chosen is
Supplier G J S O U
Probability 0.15 0.04 0.01 0.55 0.25
Generally the probability that company G , J , S are chosen is
[tex]P(G , J , S ) = 0.15 + 0.04 + 0.01[/tex]
=> [tex]P(G , J , S ) = 0.20[/tex]
Generally the probability that company O, U are chosen is
[tex]P(O, U ) = 0.55+ 0.25[/tex]
=> [tex]P(O, U ) = 0.80[/tex]
Generally the probability that supplier S will be chosen given that suppliers O and U are both ultimately not chosen is mathematically represented as
[tex]P(S | (O ,U)' ) = \frac{ P(S \ n \ (O , U)' )}{ P((O, U)')}[/tex]
[tex]P((O, U)' = 1 - P(O , U)[/tex]
[tex]P((O, U)' = 1 - 0.8[/tex]
[tex]P((O, U)' =0.2[/tex]
And
[tex]P(S \ n \ (O , U)' ) = P(S) = 0.01[/tex]
=> [tex]P(S | (O ,U)' ) = \frac{ 0.01 }{ 0.2}[/tex]
=> [tex]P(S | (O ,U)' ) = 0.05[/tex]
