Question

A dice with 4 triangular faces having numbers 1, 2, 3, 4, is rolled 5 times. What is the probability that all the 4
numbers on the faces appear on the top at least once?​

Answer 1

Answer:

1/4is the probability

Answer 2

Given: A dice with 4 triangular faces having numbers $1,2,3,4$ is rolled $5$ times.

To find: The probability that all the 4 numbers on the faces appear at least once.

Solution:

It is said that a die with 4 triangular faces is rolled $5$ times,

∴ The total outcomes that the die can have $=4*4*4*4*4=1024$

Now when a die is rolled 4 times there has to be one outcome that is independent.

Probability of the outcome that is independent $=4C_1$

The other outcomes will come in order that is one by one which is $=3C1,2C1,1C1$

For the rearrangement of the die, it can be arranged in $\frac{5!}{2!}$ ways since the two outcomes of the die will be the same always.

∴ Probability that the 4 faces on the die will appear on the top for at least one,

$P=\frac{4C1*3C1*2C1*1C1*4C1*\frac{5!}{2!} }{1024}$

$P=\frac{96*\frac{5!}{2!} }{1024}$

$P=\frac{5760}{1024}$

Final answer:

The probability that all 4 faces appear on the top at least once is $\frac{5760}{1024}$