you pick a card at random. without putting the first card back, you pick a second card at random. what is…

you pick a card at random. without putting the first card back, you pick a second card at random. what is the probability of picking a 1 and then picking a 2? simplify your answer and write it as a fraction or whole number.

you pick a card at random. without putting the first card back, you pick a second card at random. what is the probability of picking a 1 and then picking a 2? simplify your answer and write it as a fraction or whole number.

Answer

Explanation:

Step1: Calculate probability of first - pick

There are 3 cards initially. The probability of picking a 1 on the first pick is $\frac{1}{3}$ since there is 1 card labeled 1 out of 3 cards.

Step2: Calculate probability of second - pick

After picking a 1 and not replacing it, there are 2 cards left. The probability of picking a 2 on the second pick is $\frac{1}{2}$ since there is 1 card labeled 2 out of the remaining 2 cards.

Step3: Calculate combined probability

For dependent events, we multiply the probabilities of each event. So the probability of picking a 1 first and then a 2 is $\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$