Question

For the chance to be team captain, the numbers 1-30 are put in a hat and you get two chances to pick a number, without replacement. Which formula correctly shows how to find the probability that you choose the number 1 and then 2?

Answer 1

The formula to find the probability is P(A ∩ B)=P(B | A)P(A) and P(A ∩ B) =
`(1)/(870)`.

Explanation:

Total numbers in the hat = 30

Let A be the event of picking number 1 and B be the event of picking number 2 then without replacement.

Clearly, the probability of the second event depends on the first event.

So, P(A ∩ B)=P(B | A)P(A)

P(A) =
`(1)/(30)`

P(B | A) means probability of event B with the condition that event A has happened.

So, the first number picked is 1.

Therefore, P(B | A) =
`(1)/(29)`

P(A ∩ B)=
`((1)/(29) )((1)/(30) )`

`=(1)/(870)`