GATE Computer Science (CS) 2018 Shift 1 Solved Paper

Question : 9 of 65

Marks: +1, -0

A six sided unbiased die with four green faces and two red faces is rolled seven times. Which of the following combinations is the most likely outcome of the experiment?

Three green faces and four red faces.
Four green faces and three red faces.
Five green faces and two red faces.
Six green faces and one red face.

Validate

Solution:

Four green, two red face

P(G)=\;{4}/{6}=\;{2}/{3}

q(R)=\;{1}/{3}

n=7

Option (1),

P(G=3)={ }^{7} C_{3}(\;{2}/{3})^{3}(\;{1}/{4})^{4}

=\;{35 × 2^{3}}/{(3)^{7}}=\;{35 × 2^{3}}/{(3)^{7}}

(2),

{P}( {G}=4)={ }^{7} {C}_{4} ×(\;{2}/{3})^{4} ×(\;{1}/{3})^{3}

=\;{35 × 2^{4}}/{(3)^{7}}=\;{35 × 2^{4}}/{(3)^{7}}

(3),

{P}( {G}=5)={ }^{7} C_{5} ×(\;{2}/{3})^{5} ×(\;{1}/{3})^{2}

=\;{21 × 2^{5}}/{(3)^{7}}=\;{42 × 2^{4}}/{(3)^{7}}

(4),

{P}( {G}=6)={ }^{7} C_{6} ×(\;{2}/{3})^{6} ×(\;{1}/{3})

=\;{7 × 2^{6}}/{(3)^{7}}=\;{28 × 2^{4}}/{(3)^{7}}

Option 3 is maximum value.
So, five green faces and two red faces.

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