Fill in the blanks:If X follows binomial distribution with parameters

1.	Fill in the blanks:If X follows binomial distribution with parameters n = 5, p and P (X = 2) = 9.P (X = 3), then p = ___________
Answer» p = 1/10 As n = 5 {representing no. of trials} p = probability of success As it is a binomial distribution. ∴ probability of failure = q = 1 – p Given, P(X = 2) = 9.P(X = 3) The binomial distribution formula is: P(x) = _nC_x P^x (1 – P)^{n – x} Where: x = total number of “successes.” P = probability of success on an individual trial n = number of trials Using binomial distribution, ⇒ ⁵C₂p²q^5-2 = 9⁵C₃p³q^5-3 ⇒ 10p²q³ = 9×10p³q² ⇒ 10q = 90p {As , p≠0 and q ≠ 0} ⇒ q = 9p ⇒ 1-p = 9p ⇒ 10p = 1 ∴ p = 1/10

Fill in the blanks:If X follows binomial distribution with parameters n = 5, p and P (X = 2) = 9.P (X = 3), then p = ___________

Answer»

p = 1/10

As n = 5 {representing no. of trials}

p = probability of success

As it is a binomial distribution.

∴ probability of failure = q = 1 – p

Given,

P(X = 2) = 9.P(X = 3)

The binomial distribution formula is:

P(x) = _nC_x P^x (1 – P)^{n – x}

Where:

x = total number of “successes.”

P = probability of success on an individual trial

n = number of trials

Using binomial distribution,

⇒ ⁵C₂p²q^5-2 = 9⁵C₃p³q^5-3

⇒ 10p²q³ = 9×10p³q²

⇒ 10q = 90p {As , p≠0 and q ≠ 0}

⇒ q = 9p

⇒ 1-p = 9p ⇒ 10p = 1

∴ p = 1/10

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