you pick a card (3, 4, 5, 6) at random. without putting the first card back, you pick a second card at…

you pick a card (3, 4, 5, 6) at random. without putting the first card back, you pick a second card at random. what is the probability of picking a 5 and then picking a 6?

you pick a card (3, 4, 5, 6) at random. without putting the first card back, you pick a second card at random. what is the probability of picking a 5 and then picking a 6?

Answer

Explanation:

Step1: Calculate probability of picking 5 first

There are 4 cards in total. The probability of picking a 5 on the first - draw is $\frac{1}{4}$.

Step2: Calculate probability of picking 6 second

Since the first card is not replaced, there are 3 cards left. The probability of picking a 6 on the second - draw, given that a 5 was picked first, is $\frac{1}{3}$.

Step3: Calculate joint probability

The probability of two dependent events occurring is the product of their individual probabilities. So the probability of picking a 5 and then a 6 is $\frac{1}{4}\times\frac{1}{3}=\frac{1}{12}$.

Answer:

$\frac{1}{12}$