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# State whether the following is True or False : If X ~ B(n,p) and n = 6 and P(X = 4) = P(X = 2) then p = 12 - Mathematics and Statistics

MCQ
True or False

State whether the following is True or False :

If X ~ B(n,p) and n = 6 and P(X = 4) = P(X = 2) then p = (1)/(2)

#### Options

• True

• False

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#### Solution

True
Given, n = 6, P(X = 4) = P(X = 2)
X ~ B(n, p) ≡ X ~ B (6, p)
The p.m.f. of X is given by
p(X = x) = ""^"n""C"_x "p"^x q^("n" - x)
∴ p(X = x) = ""^6"C"_x "p"^x q^(6 - x), x = 0, 1, 2, ..., 6
Now, P(X = 4) = P(X = 2)
∴ ""^6"C"_4 "p"^4 "q"^2 = ""^6"C"_2 "p"^2 "q"^4

∴ (6!)/(4!2!) "p"^2 = (6!)/(2!4!) "q"^2

∴ p2 = q2
∴ p = ± q
∴ p =q
∴ p = 1 – p          ...[∵ q = 1 – p ]
∴ p + p = 1
∴ 2p = 1
∴ p = (1)/(2).

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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Miscellaneous Exercise 8 | Q 3.07 | Page 154
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