Discrete Mathematics
(a).
Let the Event A = Drivers given the breath test for drunk driving
Event B = Drivers given the blood test for drunk driving
(b)
Probability of event A = P(A) = 90% = "\\frac {90} {100} = 0.9"
Probability of event B = P(B) = 11% = "\\frac {11}{100} = 0.11"
P(A ∩ B)= 8% = 0.08
(c).
P(A ∩ B)= The probability that the drivers stopped on suspicion of drunk driving are both given both breath test
and blood test
(d)
If P(A ∩ B)= 0, then A and B are disjoint events .
Here, P(A ∩ B)= 0.08
So, A and B are not disjoint events.
(e)
If "P(A \u2229 B)= P(A) \\times P(B)," then A and B are independent events.
P(A ∩ B)= 0.08
"P(A) \\times P(B) = 0.9 \\times 0.11 = 0.099"
"P(A \u2229 B) \\ne P(A) \\times P(B)"
Answer: So, A and B are not independent events.
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