you pick a card at random. without putting the first card back, you pick a second card at random.\n2 3 4…

you pick a card at random. without putting the first card back, you pick a second card at random.\n2 3 4 5\nwhat is the probability of picking a prime number and then picking a prime number?\nsimplify 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.\n2 3 4 5\nwhat is the probability of picking a prime number and then picking a prime number?\nsimplify your answer and write it as a fraction or whole number.

Answer

Explanation:

Step1: Identify prime - numbers and total numbers

The numbers are 2, 3, 4, 5. Prime numbers are 2, 3, 5. So there are 3 prime numbers out of 4 numbers.

Step2: Calculate the first - pick probability

The probability of picking a prime number on the first pick is $P_1=\frac{3}{4}$.

Step3: Calculate the second - pick probability

Since we do not put the first card back, there are 3 cards left. If the first card was prime, then there are 2 prime numbers left. So the probability of picking a prime number on the second pick given that the first pick was prime is $P_2=\frac{2}{3}$.

Step4: Calculate the combined probability

For two dependent events, the probability of both events occurring is $P = P_1\times P_2$. So $P=\frac{3}{4}\times\frac{2}{3}=\frac{6}{12}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$