Question

A die is rolled 5 times. What is the probability that 1 occurs twice, 2, 3 and 4 occur once each, and 5 and 6 do not occur (round off to fourth decimal place)

Answer 1

Answer:

0.0077

Step-by-step explanation:

From the given information;

Each outcome possesses the same probability of 1/6 in a single roll.

The required probability can be estimated by using the multinomial distribution;

Therefore;

$P = \dfrac{5!}{2!\times 1!\times 1!\times\times 1! }\times (\dfrac{1}{6})^2\times (\dfrac{1}{6})\times (\dfrac{1}{6})\times (\dfrac{1}{6})$

$P = 60\times (\dfrac{1}{36})\times\dfrac{1}{216}$

P = 0.0077

The required probability = 0.0077     to 4 decimal decimals