a batch of tiles, shown below, is placed into a bag. ariana randomly draws one tile from the bag, records…

a batch of tiles, shown below, is placed into a bag. ariana randomly draws one tile from the bag, records it, puts it back in the bag, and draws another tile. what is the probability that ariana will draw a purple tile first and a red tile second?\na. 17/60\nb. 1/30\nc. 1/5\nd. 1/60

a batch of tiles, shown below, is placed into a bag. ariana randomly draws one tile from the bag, records it, puts it back in the bag, and draws another tile. what is the probability that ariana will draw a purple tile first and a red tile second?\na. 17/60\nb. 1/30\nc. 1/5\nd. 1/60

Answer

Answer:

B. 1/30

Explanation:

Step1: Count total tiles

There are 5 rows and 12 columns, so total tiles = $5\times12 = 60$.

Step2: Find probability of drawing purple first

There are 4 purple tiles. Probability of drawing purple first, $P(purple)=\frac{4}{60}=\frac{1}{15}$.

Step3: Find probability of drawing red second

There are 12 red tiles. Probability of drawing red second, $P(red)=\frac{12}{60}=\frac{1}{5}$.

Step4: Calculate combined probability

Since the draws are independent events, we multiply probabilities. $P(purple\ then\ red)=\frac{1}{15}\times\frac{1}{5}=\frac{1}{30}$.