Question

if a dice is rolled 10 times what is the probability that 2 will appear 4 times

Answer 1

25% of getting 2 it is so easy to find

Answer 2

If a dice is rolled 10 times The probability that 2 will appear 4 times is 0.054266

Given:

A dice is rolled 10 times

To Find:

The probability that 2 will appear 4 times

Solution:

$P(x) = {^n}C_xp^x(1-p)^{n-x}$

where n = total = 10

x = expected occurrence = 4

p = probability of event  = 1/6

 (As dice has 6 numbers so probability of appearing 2 is 1/6)

1 - p  = q  = 1 - 1/6  = 5/6

Substituting values

$P(4) = {^{10}}C_4(\frac{1}{6} )^4(\frac{5}{6} )^{10-4}$

¹⁰C₄ = 210

P(4) = 210 * 5⁶/6¹⁰

P(4) ≈ 0.054266

The probability that 2 will appear 4 times is 0.054266

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