MODELING REAL LIFE On a game show, a contestant randomly draws a chip from a bag and replaces it. The theoretical probability of drawing a winning chip is \( \frac{3}{10} \). The bag contains 9 winning chips. a. How many chips are in the bag? b. Out of 20 contestants, how many do you expect to draw a winning chip? chips contestants

To find the total number of chips in the bag, we can set up the proportion based on the theoretical probability. Since the probability of drawing a winning chip is \( \frac{3}{10} \) and there are 9 winning chips, we can set up the equation: \( \frac{9}{x} = \frac{3}{10} \), where \( x \) is the total number of chips. Solving for \( x \) gives us \( x = 30 \). So, there are 30 chips in the bag. Now, if we look at the expected number of contestants out of 20 who will draw a winning chip, we can use the probability to determine this. Since the probability of drawing a winning chip is \( \frac{3}{10} \), we multiply this probability by the number of contestants: \( 20 \times \frac{3}{10} = 6 \). Therefore, out of 20 contestants, we expect 6 to draw a winning chip.