you pick a card at random. without putting the first card back, you pick a second card at random.\n5 6 7…

you pick a card at random. without putting the first card back, you pick a second card at random.\n5 6 7 8\n9\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.\n5 6 7 8\n9\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

Answer:

$\frac{1}{10}$

Explanation:

Step1: Identify prime - numbers

Prime numbers among 5, 6, 7, 8, 9 are 5 and 7. So there are 2 prime numbers out of 5 numbers.

Step2: Calculate first - pick probability

The probability of picking a prime number on the first pick is $\frac{2}{5}$ since there are 2 prime numbers out of 5 total numbers.

Step3: Calculate second - pick probability

Since we don't put the first card back, for the second pick, there are 4 numbers left. If the first number was prime, then there is 1 prime number left. So the probability of picking a prime number on the second pick given that the first pick was prime is $\frac{1}{4}$.

Step4: Calculate combined probability

By the multiplication rule for independent events (in the non - replacement case, conditional probability), the probability of picking a prime number and then another prime number is $\frac{2}{5}\times\frac{1}{4}=\frac{2}{20}=\frac{1}{10}$.