help please

it is math course

17. Mariam is exploring sports-apparel sales for any particular trends. As part of her analysis, she would first like to examine whether the age of the customer matters when buying compression clothing. She collects data on 600 recent purchases in the compression-gear market. She cross-classifies the data by age group and brand name, as shown below. Brand Name Age Group Under Armour Nike Adidas Under 35 years 174 132 90 35 years and older 54 72 78 (a) What is the probability that a randomly selected customer is younger than 35 years old? (b) What is the probability that a randomly selected customer purchases a Nike garment? (e) What is the probability that a customer is younger than 35 years old and purchases a Nike garment? (d) What is the probability that a customer is either younger than 35 years old or purchases a Nike garment? (e) What is the probability that a customer is under 35 years of age, given that the customer purchases a Nike garment? () What is the probability that a customer purchases a Nike product, given that the cus- tomer is under 35 years of age? (8) Determine whether the events under 35 years old" and "Nike" are independent. Justify your answer using relevant probabilities