Question

An urn contains 8 balls : 4 red , 2 blue and 2 green. Now n balls are drawn out of the urn. Calculate the probability that out of n drawn balls exactly x balls are red.

Answer 1

Answer:

$p(a) = \frac{3}{8}$

Given:-

urn contain 8 balls

• 4 red ball
• 2 blue ball
• 2 green ball

to find:-

• the probability that out of n drawn balls exctly balls are red

as per condition,

S ={R,R,R,B,B,G,G}

n(s) =8

now,

as per condition

drawn from urn are exctly red ball

A ={R,R,R}

n(A) =3

$p(a) = \frac{n(a)}{n(s)} \\ \\ p(a) = \frac{3}{8}$

Answer 2

P(x) = ⁿCₓ/2ⁿ is the probability that out of n drawn balls exactly x balls are red.

Step-by-step explanation:

An urn contains 8 balls : 4 red , 2 blue and 2 green

Probability of Red Balls = 4/8 = 1/2

Probability of Not Red Ball = 1 - 1/2 = 1/2

if n Balls are drawn then probability of exactly x balls

P(x) = ⁿCₓ(p)ˣ(q)ⁿ⁻ˣ

=> P(x) = ⁿCₓ(1/2)ˣ(1/2)ⁿ⁻ˣ

=>  P(x) = ⁿCₓ(1/2)ⁿ

=>   P(x) = ⁿCₓ/2ⁿ

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