Drake has rectangular, circular, star-shaped, and heart-shaped stickers in a box. Drake conducts a probability experiment in which for each event, he randomly draws one sticker from the box, records its shape, and then replaces it. The results are shown in the table.
Shape Frequency
Rectangular 8
Circular 24
Star-shaped 52
Heart-shaped 36
Based on the probability model, how many of each shape of sticker are likely to be in the box if there are a total of 30 stickers?
Based on the frequencies provided, we can calculate the probabilities of drawing each shape of sticker:
- Probability of drawing a rectangular sticker = 8/120 = 1/15
- Probability of drawing a circular sticker = 24/120 = 1/5
- Probability of drawing a star-shaped sticker = 52/120 = 13/30
- Probability of drawing a heart-shaped sticker = 36/120 = 3/10
If there are a total of 30 stickers in the box, we can estimate the number of each shape of sticker likely to be in the box by multiplying the total number of stickers by the probability of drawing each shape:
- Number of likely rectangular stickers = (1/15) * 30 = 2
- Number of likely circular stickers = (1/5) * 30 = 6
- Number of likely star-shaped stickers = (13/30) * 30 = 13
- Number of likely heart-shaped stickers = (3/10) * 30 = 9
Therefore, based on the probability model, there are likely 2 rectangular stickers, 6 circular stickers, 13 star-shaped stickers, and 9 heart-shaped stickers in the box if there are a total of 30 stickers.