Question

You pick a card at random. Without putting the first card back, you pick a second card at random.1234What is the probability of picking a 4 and then picking a number less than 3?Simplify your answer and write it as a fraction or whole number.

Answer 1

The probability of picking a 4 in the first selection is:

$P(4)=\frac{1}{4}$

Now we only have the cards 1, 2, and 3 in the deck.

The probability of picking a number less than 3, that is, 1 or 2 is:

$P(\lt3)=\frac{2}{3}$

The combined (dependent) probability is the product of the individual probabilities:

$P=\frac{1}{4}\cdot\frac{2}{3}=\frac{1}{6}$

The probability is 1/6