Answer to Question #98476 in Discrete Mathematics for Ahmed

Question #98476
Police report that 90% of drivers stopped on suspicion of drunk driving are given a
breath test, 11% are given a blood test, and 8% are given both.
(a) In this context, define two events A and B.
(b) Write the given information in probability notation.
(c) Explain, in this context, the meaning of P(A ∩ B).
(d) Are A and B disjoint events?
(e) Are A and B independent events?
1
Expert's answer
2019-11-12T10:13:35-0500

Probabilities of an Events

(a).


Event A = a drunk driving are given a breath test.


Event B = a drunk driving are given a blood test.


(b).


P(A) = 90% ="\\frac{90} {100} =0.9"



P(B ) = 11% = "\\frac {11} {100} = 0.11"



P(Both) = "P(A\\bigcap B ) = 8"% = "\\frac{8} {100} = 0.08"


(c).


"P(A\\bigcap B ) =" The probability that the drivers stopped on suspicion of drunk driving are given both

breath test AND blood test.

(d).

We knows, If the Events A and B are Disjoint, we can write as

"P(A\\bigcap B) = 0"

But, Here "P(A\\bigcap B) = 0.08 \\ne 0"


So, the Events A and B are not disjoint


(e).


If the events A and B are independent, then "P(A\\bigcap B) = P(A) \\times P(B)"



Here,

"P(A\\bigcap B ) = 0.08 \\space and \\space P(A) \\times P(B) = 0.9 \\times 0.11 = 0.099"

So,

"P(A\\bigcap B) \\ne P(A) \\times P(B)"

So, the events A and B are not Independent

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