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 5 and then picking an even number? 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 5 and then picking an even number? write your answer as a fraction or whole number.

Answer

Explanation:

Step1: Calculate probability of picking 5 first

There are 8 cards in total. The probability of picking a 5 on the first - draw is $\frac{1}{8}$ since there is 1 card with the number 5 out of 8 cards.

Step2: Calculate probability of picking an even number second

After picking a 5 on the first draw (without replacement), there are 7 cards left. The even - numbered cards are 2, 4, 6, 8, so there are 4 even - numbered cards out of 7 remaining cards. The probability of picking an even number on the second draw is $\frac{4}{7}$.

Step3: Calculate the joint probability

Since these are dependent events, the probability of both events occurring is the product of their individual probabilities. So the probability is $\frac{1}{8}\times\frac{4}{7}=\frac{4}{56}=\frac{1}{14}$.

Answer:

$\frac{1}{14}$