Question

Liam knows there are only blue or red same-sized color tiles in a bag. He selects a tile at random, records the color, and places the tile back in the bag. Liam does this 30 times and selects a blue tile 12 times. What is the probability of selecting a red tile on the next draw?

Answer 1

After 30 draws, with 12 being blue, the remaining 18 must be red. Therefore, the probability of Liam drawing a red tile on his next draw is 18/30, which reduces to 3/5 or a 60% chance (0.6 as a decimal).

Step-by-step explanation:

The probability of selecting a red tile after Liam has selected blue tiles 12 times out of 30 draws is determined by looking at the relative frequency of selecting a red tile. Since he drew 30 tiles and 12 were blue, we can infer that 18 were red (since there are only blue and red tiles).

The probability of drawing a red tile is the number of red tiles drawn divided by the total number of tiles drawn. Thus, the probability of selecting a red tile on the next draw is:

Probability of red tile = Number of red tiles drawn / Total number of draws

Probability of red tile = 18 / 30 = 3/5 = 0.6

So, there is a 60% chance, or a probability of 0.6, that Liam will draw a red tile on his next draw.