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

Answer:

The formula to find the probability is P(A ∩ B)=P(B | A)P(A) and P(A ∩ B) = $\frac{1}{870}$.

Step-by-step 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) = $\frac{1}{30}$

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) = $\frac{1}{29}$

P(A ∩ B)=$(\frac{1}{29} )(\frac{1}{30} )$

$=\frac{1}{870}$