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 events. the probability that the numbers on both tiles are odd is 1/4.

Explanation:

Step1: Determine odd - numbered tiles

The odd - numbered tiles among 1 - 10 are 1, 3, 5, 7, 9. So there are 5 odd - numbered tiles out of 10 tiles.
The probability of selecting an odd - numbered tile on the first draw, $P(A)=\frac{5}{10}=\frac{1}{2}$.

Step2: Since the tile is replaced

The probability of selecting an odd - numbered tile on the second draw, $P(B)=\frac{5}{10}=\frac{1}{2}$.

Step3: Use the multiplication rule for independent events

Since the two draws are independent events (because the tile is replaced), the probability that both events occur is $P(A\cap B)=P(A)\times P(B)$.
$P(A\cap B)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

The probability that the numbers on both tiles are odd is $\frac{1}{4}$, and selecting the first tile and selecting the second tile are independent events.