1.Sixty people are recruited to participate in a Pepsi versus Coke taste test trial. The trial participants will be asked to taste a sample of both Pepsi and Coke (in a random order) and then to indicate which sample they prefer.

Prior to performing this taste test trial, the researcher claims that 28% of people will prefer Pepsi to Coke. Based on this claim, determine the probability (to 4 decimal places) that:

1. fewer than twenty-five participants prefer Pepsi

2. at least 22 people but no more than 30 participants preferred Pepsi

2.

The probability a car is serviced under warrantyisknown to be36%and the probability a car being a fully imported model is25%.The probability a car is serviced underwarranty and is a fully imported model is10%.What is theprobabilitya car is imported or serviced under warranty?(2 decimal places)

3.

To ascertain the effectiveness of a new, quicker, and simpler test for identifying diabetes, a study was undertaken involving 883 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:

• 318 of the participants knew they had diabetes, with the other participants definitely not having diabetes.
• 21 participants knew they had diabetes and produced a negative test result.
• 522 participants produced a negative test result.

A participant from the study is chosen at random. What is theprobabilitythe participant does not actually have diabetes given the test result is positive? (3 decimal places)

4.

The industry standards suggest that 23% of new vehicles require warranty service within the first year. A dealer sold24 Nissans yesterday. What is theprobabilitythat3 of these vehicles require warranty service? (3 decimal places)

5.

Consider two events X and Y that have marginal probabilities of 0.69 and 0.52 respectively. Their joint probability is 0.46. Calculate theprobabilitythat event X occurs if Y has occurred. (3 decimal places)

6.

1. Thenumbershowingontheupperfaceofafairsix-sideddiceisobservedwhenrolled.ConsidereventsAandBdefinedas:

   • A=thenumberobservedisatmost2
   • B=thenumberobservedisanevennumber
2. Find
3. 1.P(A')(3 decimal places)
4. 2. P(A or B)(3 decimal places)