During a promotional event at the local shopping mall, qualified customers receive complimentary gifts. For each $900 a customer spends, she is eligible to receive one gift (for example: if she spends a total of $4,500, she can get 5 gifts). There are 5 types of gifts: headphones, wireless headphones, Bluetooth speakers, iPads, and iPhones. 40% of the gifts are headphones, 20% of the gifts are wireless headphones, 20% of the gifts are Bluetooth speakers, 10% are iPhones, and the remaining are iPads. Assume the gifts are assigned randomly. Sandy spends $10,800 in total at the shopping mall.

a. (4 points) Use the Binomial formula (show your calculations) to calculate the probability that Sandy receives exactly two iPads.

b. (3 points) Given that for the first 4 gifts Sandy does not receive an iPhone, what is the probability that in the remaining gifts at least one of them is an iPhone? Use the table of binomial probabilities attached.

TABLE C Binomial probabilities TABLE C Binomial probabilities (continued) Entry is P(X - k) - (x)'(1 - pr Entry is PO - k) - (x) p'(1 - py N : ANDHAWNNO VONAWN-DOUAWN-O MANN- O . * NOWAWN - O N ( Continued )TABLE C Binomial probabilities (continued) TABLE C Binomial probabilities (continued) Entry is P(x - *) - (#)p'(1 - p5- Entry is P(X - 4) - (* )p'(1 - pr BomVanAWNNO 12 (Continued