the questions is all about probability

. A bakery has 24 croissants, each lled with one of chocolate, raspberry, apricot, or marzipan lling. A cus- tomer selects 4 croissants at random. If there are 6 croissants with each type of lling, what is the probability the customer ends up with exactly two types of croissants? [4] . Suppose an 8digit code is generated at random (each digit any of 0-9). Let E be the event that the code contains at least one 0 and let F be the event that it contains no 9s. Use an appropriate equation to determine whether or not E and F are independent. [4] . Urn A contains 3 red balls and 4 yellow balls. Urn B contains 1 red ball and 6 purple balls. An urn is selected at random and a ball is drawn without replacement. If the ball is red, a second ball is drawn from the same urn. Otherwise the second ball is drawn from the opposite urn. What is the probability that exactly one red ball is drawn? [4] . The following table gives information about customers at an optometrist ofce who made a warranty claim on their eye glasses in the previous year. Age (years) Number of clients Proportion with a warranty claim Under 20 20% 20-39 45% 40-59 60% 60-79 80% 80 and Older 90% A person is selected at random and found to have made a warranty claim on their glasses in the previous year. What is the probability the person is 20-39 years old? [4]