Question

flo thinks she may be able to increase sales if she makes a big show of flipping pancakes at her diner. but flipping pancakes high in the air takes a lot of practice! a. after flipping 35 pancakes, only 22 landed correctly on the grill. what is the probability (expressed in percent) of flo correctly flipping a pancake? hint (a) b. flo needs 42 pancakes for a large hungry group that just arrived. how many pancakes should she attempt to flip so that 42 flip correctly? hint (b) c. a customer orders a side of “flos grab bag of flapjacks” in which a customer gets one randomly chosen pancake. flo has prepared a pan of 12 sourdough pancakes and 15 buttermilk pancakes. how many banana pancakes should flo add to the pan if she wants the probability of randomly grabbing one banana pancake to be $\frac{1}{10}$? hint (c)

Explanation:

Step1: Calculate probability for part a

The probability formula is $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Here, the number of favorable outcomes (correctly - flipped pancakes) is 22 and the total number of outcomes (total pancakes flipped) is 35. So, $P_a=\frac{22}{35}$. To convert it to a percentage, we multiply by 100: $P_a=\frac{22}{35}\times100=\frac{2200}{35}\approx 62.86\%$.

Step2: Solve for part b

Let the number of pancakes she should attempt to flip be $x$. We know from part a that the probability of correctly - flipping a pancake is $P = \frac{22}{35}$. We want 42 pancakes to flip correctly. Using the proportion $\frac{22}{35}=\frac{42}{x}$. Cross - multiply: $22x=42\times35$. Then $x=\frac{42\times35}{22}=\frac{1470}{22}\approx 66.82$. Since we can't flip a fraction of a pancake, she should attempt to flip 67 pancakes.

Step3: Solve for part c

Let the number of banana pancakes be $x$. The total number of non - banana pancakes is $12 + 15=27$. The total number of pancakes after adding $x$ banana pancakes is $x + 27$. We want the probability of choosing a banana pancake to be $\frac{1}{10}$. So, $\frac{x}{x + 27}=\frac{1}{10}$. Cross - multiply: $10x=x + 27$. Subtract $x$ from both sides: $10x−x=27$, $9x=27$, and $x = 3$.

Answer:

a. Approximately $62.86\%$
b. 67
c. 3