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 4 and then picking a number less than 4?

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 4 and then picking a number less than 4?

Answer

Explanation:

Step1: Calculate probability of picking 4 first

There are 4 cards in total. The probability of picking a 4 on the first - draw is $P_1=\frac{1}{4}$.

Step2: Calculate probability of picking a number less than 4 second

After picking a 4 on the first draw (without replacement), there are 3 cards left. The numbers less than 4 among the remaining cards are 3, so there is 1 such card. The probability of picking a number less than 4 on the second draw given that a 4 was picked first is $P_2 = \frac{1}{3}$.

Step3: Calculate the joint - probability

Since these are dependent events, the probability of both events occurring is the product of their individual probabilities. Using the formula for the probability of dependent events $P = P_1\times P_2$. So $P=\frac{1}{4}\times\frac{1}{3}=\frac{1}{12}$.

Answer:

$\frac{1}{12}$