Two cellphone companies operate in a given city, the X company and the Y company. The X company is more popular than the Y company, as you know that 70% of the users belong to the X company and the remaining 30% belong to the Y company. A cell call was involved in a hit and run accident at night. A witness identified the cellphone involved had the product icon from the Y company. The court tested the appearance of products from the two companies under similar visibility conditions. When testing a sample of cellphones, the court found some identification errors can occur due to similar design of the cellphone products from the two companies. Only 80% of the Y company cellphones appeared to be correctly identified, and 20% of the Y company cellphones were misclassified as a product from the X company. Only 75% of the X company cellphones appeared to be correctly identified, and 25% of the X company cellphones were misclassified as a product from the Y company. Hence, even though the witness identified the cellphone as a produce from the Y company, it could have belonged to the X company. Use Bayes rule to compute the probability that the phone is truly from company Y given the witness's report, P(the phone is from company Y | witness identified the phone from company Y)? Make sure that you show your work.