# Statistics

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## Probability, Discrete Random Variables and Continuous Random Variables

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• Bag A contains 9 red marbles and 3 green marbles. Bag B contains 9 black marbles and 6 orange marbles. Find the probability of selecting one green marble from bag A and one black marble from bag B.
• A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. Two marbles are selected. Draws are made without replacement. Find P(1st orange then green).
• A bag contains 5 red marbles and 4 pink marbles. A marble is randomly drawn and then replaced. What is the probability the first marble is pink and the second is red?
• Two fair dice are rolled. Determine the probability of obtaining exactly two sixes.
• Two fair dice are rolled. Determine the probability of obtaining a sum greater than six.
• A delegation of six students is to be selected from a group of 10 girls and 8 boys. Determine the probability that equal numbers of girls and boys are chosen.
• A fair die is tossed. Calculator the probability of obtaining a prime number.
• Three fair coins are tossed. Calculate the probability of obtaining exactly 2 heads.
• A fair octagonal die, labelled A, B, C, D, E, F, G and H is rolled twice. Calculate the probability of obtaining a vowel and a consonant.
• A box contains 5 red and 15 green balls. Four balls are chosen with replacement from this box. Find the probability of 3 red balls chosen.
• A box contains 5 red and 15 green balls. Four balls are chosen without replacement from this box. Find the probability of 3 red balls chosen.
• If a discrete random variable has an expected value E(X)=12 and a standard deviation of 2 determine E(2X-4) and Var(2X-4).
• Determine which one is the example of Bernoulli trial.
• Which following is not the condition for binomial distributions?
• Calculate the mean and variance of rolling a '4' on a 6 sided die.
• A binomial distribution has a mean of 360 and a standard deviation of 12. Find n and p.
• An electrical company produces switches which are packed in boxes each containing 20 switches. It is known that 4% of switches produced are defective. Find the probability that a randomly selected box has no more than one defective switch.
• The probability that John is late for school on any school day is 0.4 and it is independent of other days. For a school week of five days, find the mean number of days he will be late.
• 80% of all cats in a certain city have been bio-chipped. Fifty cats were randomly selected. Calculate the probability that at least 38 but no more than 42 have been bio-chipped.
• In a sample of 20 cats from this city, 15 were found to have been bio-chipped, while the other 5 have not been bio-chipped. 5 cats were chosen from this sample. Calculate the probability that all five cats have been bio-chipped.
• Police set up a roadblock to check cars for seatbelt use. From experience, they estimate that 80% of drivers wear seat belts. What is the probability that the second unbelted driver is in the 8th car stopped?
• Which one is not discrete random variables?
• A uniform continuous random variable X is defined over the interval 0 to 140 inclusive. Determine E(X) and Var(X).
• The travelling time between Perth and Bunbury is uniformly distributed between 90 and 120 minutes. Calculate the probability the travelling time will be exactly 100 minutes.
• The waiting time for a bus is a uniform distribution. A bus departs every 40 minutes from the bus stop. Calculate the probability that a passenger waits more than 15 minutes for the bus to depart.
• X is uniform distribution over 57 to 67 inclusive. 3 observations of X were taken. Find the probability none of these observations exceed 58.
• Which of these are not conditions for continuous random variable X?
• The life span of light bulb is normally distributed with a mean of 800 hours and a variance of 14400 hours. Find the probability that a randomly chosen light bulb has a life span that is less than 900 hours given that it exceeds 700 hours.
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