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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 75
Total: 101
Suppose X has a binomial distribution B(6,
1
2
). Show that X = 3 is the most likely outcome.
(Hint : P(X = 3) is the maximum among all P(xi),xi = 0, 1, 2, 3, 4, 5, 6)
Solution:  
Given that X has a binomial distribution B(6,
1
2
) , here n=6,p=
1
2

⇒q=1−p=
1
2

Now,
(
1
2
+
1
2
)6=6C0(
1
2
)6+6C1(
1
2
)6+...+6C6(
1
2
)6
=(
1
2
)6[6C0+6C1+...+6C6]
=(
1
2
)6[6C0+6C1+6C2+6C3+6C2+6C1+6C0]
6C3 has the maximum value in 6C0,6C1,6C2 and 6C3.
Hence 6C3(
1
2
)6 is maximum ⇒ P(X = 3) is most likely outcome.
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