Question

fill in the blank 8 points
two cards are selected from a deck of cards numbered from 1 to 10. once a card is selected, it is not replaced. what is p(two even numbers)? write the answer as a fraction in simplest form.
type your answer...

Explanation:

Step1: Identify even numbers

Numbers from 1 to 10: even numbers are 2,4,6,8,10. So there are 5 even numbers. Total cards = 10.
Probability of first even: $P_1 = \frac{5}{10}$

Step2: Probability of second even (no replacement)

After first even, remaining even numbers = 4, total remaining cards = 9.
Probability of second even: $P_2 = \frac{4}{9}$

Step3: Multiply probabilities (independent events in sequence)

$P(\text{two evens}) = P_1 \times P_2 = \frac{5}{10} \times \frac{4}{9} = \frac{20}{90} = \frac{2}{9}$

Answer:

$\frac{2}{9}$