Question

select the correct answer from each drop - down menu. a bag contains 10 tiles numbered 1 through 10. terry randomly selects a tile from the bag, replaces the tile, and then draws a second tile. when terry selects his tiles, selecting the first tile and selecting the second tile are the probability that the numbers on both tiles are odd is

Explanation:

Step1: Determine odd - number probability for one draw

The odd numbers from 1 to 10 are 1, 3, 5, 7, 9. So there are 5 odd numbers out of 10. The probability of drawing an odd - numbered tile in one draw is $P_1=\frac{5}{10}=\frac{1}{2}$.

Step2: Use the multiplication rule for independent events

Since the draws are independent (because the tile is replaced), the probability of two independent events A and B both occurring is $P(A\cap B)=P(A)\times P(B)$. Here, event A is drawing an odd - numbered tile on the first draw and event B is drawing an odd - numbered tile on the second draw. So the probability that both tiles are odd is $P = \frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$