Question

A spinner numbered 1 through 12 is spun. Find the probability that

the number spun is an 11 given that the number spun was an odd
number. Please write your answer as a fraction.

Answer 1

The probability in fraction is
`(1)/(12)`.

Explanation:

Total number of outcomes is = 12

Now we have to find the probability that spun number is 11.

That means favorable outcome is 1.

In this case, the probability can be determined by dividing the number of favorable outcomes by the total outcome. Accordingly, the total outcomes are 12 and favorable outcome is 1.

`\text{P(The spun number is 11)}= \frac{\text{Favorable outcomes}}{\text{total outcomes}} \\\text{P(The spun number is 11)}= (1)/(12) \ (in \ fraction)\\\text{P(The spun number is 11)} = 0.083 \ (in \ decimal)`

Answer 2

`(1)/(6)`

Explanation:

Let A be the event of getting an odd number.

P(A) be the probability of getting an odd number.

Total odd numbers here are 6 i.e.
`\{1,3,5,7,9,11\}`

Here, total numbers in the game are 12 i.e
`\{1,2,3,....,12\}`.

Formula for probability of an event E can be observed as:

`P(E) = \frac{\text{Number of favorable cases}}{\text {Total number of cases}}`

`P(A) = (6)/(12)\\\Rightarrow (1)/(2)`

Let B be the event of getting 11.

P(B) be the probability of getting 11.

Total number of possible cases is 1.

`P(B) = (1)/(12)`

`P(A \cap B)` is the probability that we get 11 and an odd number.

Possible number of cases = 1

`P(A\cap B) = (1)/(12)`

P(B/A) is the probability that we get an 11 given that it is an odd number.

`P(B/A) = (P(A \cap B))/(P(A))\\\Rightarrow ((1)/(12))/((1)/(2))\\\Rightarrow (1)/(6)`

Hence, P(B/A) =
`(1)/(6)`