*A wholesaler sells mandarin oranges in boxes of 60. The probability that there are X bad oranges in a box are given in the following table. Value of X 0 1 2 Probability 5k 4k 8k Calculate the value of k. Find the expected value E(X) of X. A retailer buys a box of 60 mandarin oranges for RM21 from the wholesaler. Calculate his expected profit on the box if he sells each good orange for RM0.45 after throwing away the bad ones. (a) (b) (c) 3 2k 4 k >4 0 *A woman has three keys on a ring, only one which opens the front door. As she approaches the front door, she selected one key after another at random without replacement. Draw a tree diagram to illustrate the various selections before she finds the correct key. And, construct a probability distribution table. Use this distribution to calculate the expected number of keys that she will use before opening the door.