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Yoga memberikan seperangkat kartu bridge secara ac...

Yoga memberikan seperangkat kartu bridge secara acak kepada begin mathsize 14px style 4 end style temannya yaitu Deri, Toni, dan Wawan. Setiap teman Yoga menerima begin mathsize 14px style 13 end style kartu. Peluang Wawan memperoleh kartu begin mathsize 14px style 2 end style kartu King dan kartu begin mathsize 14px style 8 end style berwarna merah adalah ...

Jawaban:

Peluang Wawan memperoleh kartu begin mathsize 14px style 2 end style kartu King dan kartu begin mathsize 14px style 8 end style berwarna merah, dapat dihitung dengan cara:

- Menentukan nilai begin mathsize 14px style straight n open parentheses straight S close parentheses end style 

S=Kejadian Wawan memperoleh begin mathsize 14px style 13 end style kartu dari begin mathsize 14px style 52 end style kartu, maka:

begin mathsize 14px style straight n open parentheses straight S close parentheses equals straight C subscript 13 superscript 52 straight n open parentheses straight S close parentheses equals fraction numerator 52 factorial over denominator 39 factorial times 13 factorial end fraction end style 

- Menentukan nilai begin mathsize 14px style straight n open parentheses straight A close parentheses end style 

A= Kejadian Wawan memperoleh begin mathsize 14px style 2 end style kartu King, kartu begin mathsize 14px style 8 end style berwarna merah, dan 2 kartu sembarang, maka:

begin mathsize 14px style straight n open parentheses straight A close parentheses equals straight C subscript 2 superscript 4 times straight C subscript 2 superscript 4 times straight C subscript 2 superscript 44 straight n open parentheses straight A close parentheses equals fraction numerator 4 factorial over denominator 2 factorial times 2 factorial end fraction times fraction numerator 4 factorial over denominator 2 factorial times 2 factorial end fraction times fraction numerator 44 factorial over denominator 42 factorial times 2 factorial end fraction end style 

- Menentukan peluang

begin mathsize 14px style straight P open parentheses straight A close parentheses equals fraction numerator straight n open parentheses straight A close parentheses over denominator straight n open parentheses straight S close parentheses end fraction straight P open parentheses straight A close parentheses equals fraction numerator fraction numerator 4 factorial over denominator 2 factorial times 2 factorial end fraction times fraction numerator 4 factorial over denominator 2 factorial times 2 factorial end fraction times fraction numerator 44 factorial over denominator 42 factorial times 2 factorial end fraction over denominator begin display style fraction numerator 52 factorial over denominator 39 factorial times 13 factorial end fraction end style end fraction straight P open parentheses straight A close parentheses equals fraction numerator 4 factorial over denominator 2 factorial times 2 factorial end fraction times fraction numerator 4 factorial over denominator 2 factorial times 2 factorial end fraction times fraction numerator 44 factorial over denominator 42 factorial times 2 factorial end fraction times fraction numerator 39 factorial times 13 factorial over denominator 52 factorial end fraction straight P open parentheses straight A close parentheses equals fraction numerator 4 times 3 times 2 factorial over denominator 2 factorial times 2 times 1 end fraction times fraction numerator 4 times 3 times 2 factorial over denominator 2 factorial times 2 times 1 end fraction times fraction numerator 44 times 43 times 42 factorial over denominator 42 factorial times 2 times 1 end fraction times fraction numerator 39 factorial times 13 times 12 times 11 times 10 times 9 times 8 times 7 times 6 times 5 times 4 times 3 times 2 times 1 over denominator 52 times 51 times 50 times 49 times 48 times 47 times 46 times 45 times 44 times 43 times 42 times 41 times 40 times 39 factorial end fraction straight P open parentheses straight A close parentheses equals fraction numerator 3.696 over denominator 6.460.893.775 end fraction end style 

Jadi, peluang Wawan memperoleh kartu begin mathsize 14px style 2 end style kartu King dan kartu begin mathsize 14px style 8 end style berwarna merah adalah begin mathsize 14px style fraction numerator 3.696 over denominator 6.460.893.775 end fraction end style.

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