Question

select the correct answer from each drop - down menu. a bag contains five tiles numbered 1 through 5. savannah randomly selects a tile from the bag, replaces the tile, and then draws a second tile. when savannah selects her tiles, selecting the first tile and selecting the second tile are dependent events. the probability that the numbers on both tiles are even is 20%.

Explanation:

Step1: Determine type of events

Since the tile is replaced after the first draw, the outcome of the first - draw does not affect the outcome of the second draw. So, the two events are independent.

Step2: Find probability of getting an even - numbered tile on a single draw

The numbers on the tiles are 1, 2, 3, 4, 5. The even - numbered tiles are 2 and 4. So, the probability of getting an even - numbered tile on a single draw is $P(\text{even})=\frac{2}{5}=0.4$.

Step3: Find probability of getting even - numbered tiles on both draws

Since the events are independent, the probability of two independent events $A$ and $B$ occurring is $P(A\cap B)=P(A)\times P(B)$. Here, $A$ is the event of getting an even - numbered tile on the first draw and $B$ is the event of getting an even - numbered tile on the second draw. So, $P(\text{even on first and even on second})=\frac{2}{5}\times\frac{2}{5}=\frac{4}{25}=0.16 = 16\%$.

Answer:

Selecting the first tile and selecting the second tile are independent events. The probability that the numbers on both tiles are even is 16%.