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 prime number and then picking a prime number? write your answer as a decimal rounded to the nearest thousandth.

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 prime number and then picking a prime number? write your answer as a decimal rounded to the nearest thousandth.

Answer

Explanation:

Step1: Count prime - numbers

The prime numbers in the set {2, 3, 4, 5, 6, 7, 8, 9} are 2, 3, 5, 7. So there are 4 prime numbers out of 8 numbers.

Step2: Calculate first - pick probability

The probability of picking a prime number on the first pick is $P_1=\frac{4}{8}=\frac{1}{2}$.

Step3: Calculate second - pick probability

Since we do not put the first card back, there are 7 cards left. If the first card was prime, then there are 3 prime numbers left. So the probability of picking a prime number on the second pick given that the first pick was prime is $P_2=\frac{3}{7}$.

Step4: Calculate combined probability

The probability of both events happening (picking a prime then another prime) is $P = P_1\times P_2=\frac{1}{2}\times\frac{3}{7}=\frac{3}{14}\approx0.214$.

Answer:

0.214