Q. 1065.0( 1 Vote )

# Fill in the blanks in the following question:

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) = _{n}C_{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,

⇒ ^{5}C_{2}p^{2}q^{5-2} = 9^{5}C_{3}p^{3}q^{5-3}

⇒ 10p^{2}q^{3} = 9×10p^{3}q^{2}

⇒ 10q = 90p {As , p≠0 and q ≠ 0}

⇒ q = 9p

⇒ 1-p = 9p ⇒ 10p = 1

**∴** **p = 1/10**

Rate this question :

A box has 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?

Mathematics - ExemplarState True or False for the statements in the Exercise.

If A, B and C are three independent events such that P(A) = P(B) = P(C) = p, then

P (At least two of A, B, C occur) = 3p^{2} – 2p^{3}

A random variable X has the following probability distribution:

Determine:

(i) K (ii) P (X < 3)

(iii) P (X > 6) (iv) P (0 < X < 3)

**OR**

Find the probability of throwing at most 2 sixes in 6 throws of a single die

Mathematics - Board PapersHow many times must a man toss a fair coin, so that the probability of having at least one head is more than 80%?

Mathematics - Board PapersAn experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes.

Mathematics - Board Papers