Respuesta :
The probability that an event A occurs (P(A)) is:
[tex]P(A)=\frac{\text{ number of favorable outcomes of A}}{\text{ number of total outcomes}}[/tex]To solve this question, follow the steps below.
Step 01: Calculate the probability the first marble is red.
Number of favorable outcomes = 5 (5 red marbles).
Number of total outcomes = 10 (10 marbles).
Then, P(red₁):
[tex]P(\text{red}_1\text{)}=\frac{5}{10}=\frac{1}{2}[/tex]Step 02: Calculate the probability the second ball is also red.
Now, let's assume that 1 red ball was removed. Then,
Number of favorable outcomes = 4 (4 red marbles remained).
Number of total outcomes = 9 (number of total marbles remained).
Then, P(red₂):
[tex]P(red_2)=\frac{4}{9}[/tex]Step 03: Calculate the probability the first and the second marbles are red.
The probability both marbles are red is the product of both probabilities.
[tex]\begin{gathered} P(\text{red)}=P(red_1)\cdot P(red_2) \\ P(\text{red)}=\frac{1}{2}\cdot\frac{4}{9} \\ P(\text{red)}=\frac{4}{18} \end{gathered}[/tex]And dividing the numerator and denominator by 4:
[tex]P(\text{red)}=\frac{\frac{4}{2}}{\frac{18}{2}}=\frac{2}{9}[/tex]Answer: The probability that both marbles he chooses are red is 2/9.
