Question

imagine ralling a fair six-sided die three times.What is the theoretical probability that all three rolls of the die show a 3 on top?D.What is the theoretical probability the first roll of the die shows a 4 and the next two rolls show a 3 on top?

Answer 1

STEP - BY - STEP EXPLANATION

What to find?

The theoretical probability that all three rolls of the die show a 3 on top.

The theoretical probability the first roll of the die shows a 4 and the next two rolls show a 3 on top.

Given:

Probability is defined as:

`probability=\frac{required\text{ outcome}}{all\text{ possible outcome}}`

Since a fair die has 6 faces, then;

P(1)= 1/6

P(2) = 1/6

P(3) = 1/6

P(4) = 1/6

P(5) = 1/6

P(6) = 1/6

a)

`P(all\text{ 3 rolls are 3\rparen=}(1)/(6)*(1)/(6)*(1)/(6)`
`=(1)/(216)`

Hence, probability that all three rolls of the die show a 3 on top is 1/216

b)

`p(first\text{ roll a 4 and the next 2 a 3\rparen= P\lparen a first roll a 4\rparen}* p(second\text{ roll }a\text{ 3\rparen}* p(third\text{ roll }a\text{ 3\rparen}`
`=(1)/(6)*(1)/(6)*(1)/(6)`

`=(1)/(216)`

Hence, probability the first roll of the die shows a 4 and the next two rolls show a 3 on top is 1/216

ANSWER

a) 1/216

b) 1/216