This is a question about the probability of different events regarding the selection of tulip bulbs. Let's solve it step by step. Note that the total number of bulbs is 28, with 10 being red, 10 being yellow, and 8 being purple.
(a) We need to find the probability that the two randomly selected tulip bulbs are both red. The probability of selecting one red bulb out of the total 28 is 10/28. Since we don't put the bulb back into the bag, the total available bulbs reduce to 27 for the second draw. The number of red bulbs also reduces to 9. So, the probability for the second draw is 9/27. The joint probability of these two draws is the product of the individual ones, approximated to 0.119.
(b) What is the probability that the first bulb selected is red and the second yellow? The probability for drawing one red bulb first is 10/28. After drawing one red bulb out, there are 27 total bulbs and 10 yellows left. So, the probability for drawing one yellow bulb next is 10/27. Again, the joint probability is the product, approximated to 0.132.
(c) Now, for the probability that the first bulb selected is yellow and the second red. The first draw probability for yellow is 10/28. After drawing one yellow bulb out of the pack, the total count reduces to 27, with 10 red bulbs left. The probability then for red on the second draw is 10/27. The joint probability, in this case, is also 0.132.
(d) Finally, for the probability that one bulb is red and the other yellow regardless of the order, we just need to add the probabilities from part (b) and part (c). Therefore, the final considerable probability is 0.264.
Remember, in the world of probability, each event is considered independently unless stated otherwise. Also, note that each figure is calculated to three decimal places.