A dice

Probability Level 1

a dice is thrown 5 times ,what is the chance that an even number will come up exactly 3 times.

5/7 1/2 5/16 none of these

Nutan Sinha by Nutan Sinha , 16, India

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1 solution

Jerry McKenzie
Feb 6, 2018

X B i n o m P D F ( p = 1 2 , n = 5 ) [ k = 3 ] = ( 5 3 ) ( 1 2 ) 3 ( 1 − 1 2 ) 5 − 3 = 5 ! 3 ! ⋅ ( 5 − 3 ) ! ⋅ ( 1 2 ) 3 ⋅ ( 1 2 ) 2 = 5 ⋅ 4 ⋅ 3 ! 3 ! ⋅ 2 ! ⋅ ( 1 2 ) 3 + 2 = 5 ⋅ 2 2 2 ⋅ 1 2 5 = 5 ⋅ 2 2 2 6 = 5 2 4 = 5 16 X~BinomPDF(p=\frac{1}{2},n=5)[k=3] \\ =\binom{5}{3}(\frac{1}{2})^3(1-\frac{1}{2})^{5-3} \\ =\frac{5!}{3!\cdot (5-3)!}\cdot (\frac{1}{2})^3\cdot(\frac{1}{2})^2 \\ =\frac{5\cdot 4\cdot 3!}{3! \cdot 2!}\cdot (\frac{1}{2})^{3+2} \\ =\frac{5 \cdot 2^{2}}{2}\cdot\frac{1}{2^{5}} \\ =\frac{5\cdot 2^{2}}{2^{6}}=\frac{5}{2^{4}}=\frac{5}{16}

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