you pick a card at random. without putting the first card back, you pick a second card at random.\nwhat is…

you pick a card at random. without putting the first card back, you pick a second card at random.\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.\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: Determine prime - numbers

The prime numbers among 1, 2, 3, 4 are 2 and 3. So there are 2 prime numbers out of 4 numbers initially.

Step2: Calculate the first - pick probability

The probability of picking a prime number on the first pick is the number of prime numbers divided by the total number of numbers. So (P_1=\frac{2}{4}=\frac{1}{2}).

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 is 1 prime number left among the 3 remaining cards. So the probability of picking a prime number on the second pick given that the first pick was prime is (P_2 = \frac{1}{3}).

Step4: Calculate the combined probability

The probability of both events happening is the product of the probabilities of each event. So (P = P_1\times P_2=\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}).

Answer:

(\frac{1}{6})