Suppose that an urn contains two different types of coupons: three coupons of type A and four coupons of type B. After Alice draws a coupon out of the urn, the urn is reset to its original state of having seven coupons: three coupons of type A and four coupons of type B (using an unlimited supply of spare coupons). Compute the expected number of draws needed for Alice to collect at least two coupons of each type (at least two of type A and at least two of type B). Do not round your answer to the nearest integer. Hint: If you need to cite basic properties (such as expectation-formula(e)) for certain probability distribution(s) as part of your work, you may do so without proof. Any random variables used should first be clearly defined.