Question

1.The number showing on the upper face of a fair six-sided dice is observed when rolled. Consider events A and B defined as:

• A = the number observed is at most 2
• B = the number observed is an even number

Find： 1.P(A') 2.P(A or B)

2.Along the road near Bundamba State High School, there are traffic lights at two different locations. At the first location, the light is green 80.9% of the time. At the second location, the light is green 79.9% of the time. The probability a vehicle gets a green light at the first location and the second location is 71.4%.   What is the probability that the light will be green at the second location if the light was green at first location? (3 decimal places)

3.Previous studies have found 30% of all people prefer Coke to all other cola drinks. A random sample of 16 people is selected. What is the probability exactly three people in this sample prefer Coke? (3 decimal places)

4.

To ascertain the effectiveness of a new, quicker, and simpler test for identifying diabetes, a study was undertaken involving 739 participants. With this test, a positive result indicates the presence of diabetes. A negative result indicates the absence of diabetes. Data collected to assess the effectiveness of this new test revealed:

• 201 of the participants confirmed they actually had diabetes, with the other participants confirming they actually did not have diabetes.
• 124 participants actually had diabetes and produced a negative test result.
• 255 participants produced a negative test result.

A participant from the study is chosen at random. What is the probability they do actually have diabetes given the test result is positive? (3 decimal places)

5.The probability that tomorrow will be a rainy day is 0.52. The probability tomorrow will be a windy day is 0.2. The probability that it will rain and be windy tomorrow is 0.07. What is the probability it will be windy or rainy or both tomorrow?  (2 decimal places)

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Answer 1

1)

A = the number observed is at most 2
B = the number observed is an even number

p(A) = 2/6 = 1/3

P(B) = 3/6 = 1/2

P(A') = 1- 1/3

= 2/3 = 0.667

NOW, P (A AND B) = 1/6

P(A or B) = P(A)+P(B)-P(A AND B)

= 1/3+1/2-1/6

= 0.667

........

2)

A= light green at 1 location

B =light green at 2nd location

P(A) = 0.809

P(B) = 0.799

P(A AND B) = 0.714

P(light will be green at the second location if the light was green at first location)

P(B|A) =

= 0.714 / 0.809

= 0.883

...................

3)

Sample size , n =    16
p =   0.3

P ( X = 3) = C (16,3) * 0.3^3 * ( 1 - 0.3)^13 =      0.146

..........

Please revert back in case of any doubt.

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