could you please help me to work out these probability quiz? thank you.

QUESTION 1

The probability a car is serviced under warranty is known to be 36% and the probability a car being a fully imported model is 25%. The probability a car is serviced under warranty and is a fully imported model is 10%. What is the probability a car is imported or serviced under warranty? (2 decimal places)

QUESTION 2

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 the probability the participant does not actually have diabetes given the test result is positive? (3 decimal places)?

QUESTION 3

The industry standards suggest that 23% of new vehicles require warranty service within the first year. A dealer sold 24 Nissans yesterday. What is the probability that 3 of these vehicles require warranty service? (3 decimal places)

QUESTION 4

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

QUESTION 5

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') (3 decimal places)

2. P(A or B) (3 decimal places)