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 6 and then picking a 7? write your answer 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 6 and then picking a 7? write your answer as a fraction or whole number.

Answer

Explanation:

Step1: Calculate first - pick probability

There are 3 cards initially. The probability of picking a 6 on the first pick is $\frac{1}{3}$.

Step2: Calculate second - pick probability

After picking a 6 on the first pick (without replacement), there are 2 cards left. The probability of picking a 7 on the second pick is $\frac{1}{2}$.

Step3: Calculate combined probability

Since these are independent - like (in the sense of sequential) events, we multiply the probabilities. So the probability of picking a 6 first and then a 7 is $\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$