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 an even number and then picking an odd number? 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 an even number and then picking an odd number? simplify your answer and write it as a fraction or whole number.

Answer

Explanation:

Step1: Calculate probability of first - pick

There are 3 even numbers (2, 4, 6) out of 6 total numbers. So the probability of picking an even number first, $P_1=\frac{3}{6}$.

Step2: Calculate probability of second - pick

After picking an even number first (without replacement), there are 5 numbers left and 3 odd numbers (3, 5, 7). So the probability of picking an odd number second given an even number was picked first, $P_2 = \frac{3}{5}$.

Step3: Calculate joint probability

Since these are dependent events, the probability of both events occurring is the product of their probabilities. So $P = P_1\times P_2=\frac{3}{6}\times\frac{3}{5}=\frac{9}{30}=\frac{3}{10}$.

Answer:

$\frac{3}{10}$