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Please can you guys answer all of the below questions with step by step solutions for all. (A) To gain a driver's licence in NSW,

Please can you guys answer all of the below questions with step by step solutions for all.

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(A) To gain a driver's licence in NSW, both a written test and a practical driving test mus be passed. Statistics show that 70% pass the written test on the first attempt, while 90% of those who sit the test a second time will pass. 60% pass their first practical te and 80% pass their second practical test. Suppose the written and practical test are independent. Calculate, as a percentage, the probability of: (i) Passing the written test on the second attempt (ii) Passing the written test after no more than two attempts (iii) Requiring a third written test (iv) Passing the practical test on the second attempt (v) Receiving a license after two written tests and one practical test (B) A bag of coloured marbles contains 7 red, 8 blue and 10 yellow marbles. 2 marbles at selected at random together in a handful. Let the discrete random variabIeX be the number of red marbles selected. (i) Create a probability distribution table for X. (ii) Find the mean, variance and standard deviation of X. (iii) Let the discrete random variable Y be the number of yellow marbles selected. Creat a probability distribution table for Y. (C) A football team has a probability of 70% of winning when Ronaldo is playing in the team. When Ronaldo is not playing, the team has a probability of 40% of winning. Th probability of the team having Ronaldo playing at any one time is 90%. Find, as a percentage correct to 2 decimal places, the probability that Ronaldo was playing when the football team won a match. FNI') (1F PAPFR

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