Answer:
[tex]Probability = 0.56[/tex]
Step-by-step explanation:
Represent the probability that Alice does well with P(A), the probability that Bob does well with P(B).
So, we have:
[tex]P(A) = 0.8[/tex]
[tex]P(B) = 0.4[/tex]
Required
Determine the probability that only one of them do well
This event is represented as: (A and B') or (B and A')
Where B' means Bob does not perform well and A' means Alice does not perform well.
And:
[tex]P(B') = 1 - P(B)[/tex]
[tex]P(A') = 1 - P(A)[/tex]
So, the probability becomes:
[tex]Probability = P(A\ and\ B')\ or\ P(B\ and\ A')[/tex]
[tex]Probability = P(A) * P(B')\ +\ P(B)*P(A')[/tex]
[tex]Probability = P(A) * (1-P(B)) +\ P(B)*(1-P(A))[/tex]
[tex]Probability = 0.8 * (1-0.4) +\ 0.4*(1-0.8)[/tex]
[tex]Probability = 0.8 * 0.6 +\ 0.4*0.2[/tex]
[tex]Probability = 0.48 + 0.08[/tex]
[tex]Probability = 0.56[/tex]
Hence, the required probability is 0.56
