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A student throws a regular tetrahedron and a die. He recorded the outcome on a possibility space. Write down the probability sample space for all possible outcomes.

Mathematics

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Step-by-step solution

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  1. Tambua matokeo yanayowezekana kwa kila tukio.

    Tetrahedron ya kawaida ina nyuso 4, kwa kawaida huhesabiwa 1, 2, 3, 4.
    Kete ya kawaida ina nyuso 6, huhesabiwa 1, 2, 3, 4, 5, 6.

  2. Orodhesha matokeo yote yanayowezekana kwa kuchanganya matokeo ya tetrahedron na kete.

    Kila matokeo yatakuwa jozi iliyoagizwa (tetrahedron, kete).

    S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)}S = \{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), \\ (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), \\ (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), \\ (4,1), (4,2), (4,3), (4,4), (4,5), (4,6)\}

    Jumla ya matokeo yanayowezekana ni 4×6=244 \times 6 = 24.

    Nafasi ya sampuli ya uwezekano ni:

    S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)}\boxed{S = \{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6)\}}
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