Question

a bag has 3 red tiles, 1 yellow tile and 2 green tiles. what is the probability that a red tile is drawn, followed by a second red tile, if the first tile is replaced?

Explanation:

Step1: Calculate total number of tiles

Total tiles = 3 + 1 + 2 = 6

Step2: Probability of first red tile

$P(\text{first red}) = \frac{\text{Number of red tiles}}{\text{Total tiles}} = \frac{3}{6} = \frac{1}{2}$

Step3: Probability of second red tile (with replacement)

Since the first tile is replaced, total tiles and red tiles remain the same:
$P(\text{second red}) = \frac{3}{6} = \frac{1}{2}$

Step4: Multiply the two probabilities

$P(\text{red then red}) = P(\text{first red}) \times P(\text{second red}) = \frac{1}{2} \times \frac{1}{2}$

Answer:

$\frac{1}{4}$