Question

You roll one 6-sided die. What is the probability of getting a 2 given you know the number is even?2313121

Answer 1

Given: A 6-sided die is given.

Required: To determine the probability of getting a 2, given you know the number is even.

Explanation: The problem is based on conditional probability.

The probability of an event X given that event Y has happened is-

`P((X)/(Y))=(P(X\cap Y))/(P(Y))`

Here, Let A be the event that outcome is an even number.

Then,

`\begin{gathered} A=\lbrace2,4,6\rbrace \\ P(A)=(3)/(6) \end{gathered}`

Let B be the event of getting 2.

Then,

`\begin{gathered} B=\lbrace2\rbrace \\ P(B)=(1)/(6) \end{gathered}`

Now,

`\begin{gathered} A\cap B=\lbrace2\rbrace \\ P(A\cap B)=(1)/(6) \end{gathered}`

Hence the probability of getting a 2, given you know the number is even, is-

`\begin{gathered} P((B)/(A))=(P(A\cap B))/(P(A)) \\ =((1)/(6))/((3)/(6)) \\ =(1)/(3) \end{gathered}`

Final Answer: The probability of getting a 2, given you know the number is even, is-

`(1)/(3)`