Question

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 a 5? write your answer as a percentage.

Explanation:

Step1: Calculate first - pick probability

There are 4 cards in total. The probability of picking a 5 on the first pick is $\frac{1}{4}$ since there is 1 card with the number 5 out of 4 cards.

Step2: Calculate second - pick probability

After picking a 5 on the first pick and not replacing it, there are 3 cards left. The probability of picking a 5 on the second pick (given that a 5 was already picked on the first pick) is 0 since there are no more 5 - numbered cards left.

Step3: Calculate combined probability

The probability of two independent events A and B occurring is $P(A)\times P(B)$. Here, the combined probability of picking a 5 first and then another 5 is $\frac{1}{4}\times0 = 0$. To convert to a percentage, we multiply by 100. So $0\times100 = 0\%$.

Answer:

0%