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Q34Section B (Section B)34 of 60

Comparisons of four labelled dice

Consider four dice D1,D2,D3D_1,D_2,D_3, and D4D_4, each having six faces marked as follows:

| Die | Marks on faces | | — | — | | D1D_1 | 4,4,4,4,0,04,4,4,4,0,0 | | D2D_2 | 3,3,3,3,3,33,3,3,3,3,3 | | D3D_3 | 6,6,2,2,2,26,6,2,2,2,2 | | D4D_4 | 5,5,5,1,1,15,5,5,1,1,1 |

In each roll of a die, each of its six faces is equally likely to occur. Suppose that each of these four dice is rolled once, and the marks on their upper faces are noted. Let the four rolls be independent. If XiX_i denotes the mark on the upper face of the die DiD_i, i=1,2,3,4i=1,2,3,4, then which of the following statements is/are correct?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Options

Select every correct option, then submit.