Question

THERE ARE 2 PARTS PLEASE ANSWER BOTH RIGHT TY HELPP!! There are 12 red cards, 17 blue cards, 14 purple cards, and 7 yellow cards in a hat.

Part A. What is the THEORETICAL probability of drawing a purple card from the hat?

Part B.
In a trial, a card is drawn from the hat and then replaced 1,080 times. A purple card is drawn 324 times. How much greater is the experimental probability than the theoretical probability?

Enter the correct answers in the boxes.

A. The theoretical probability of drawing a purple card from the hat is ______.

B. The experimental probability of drawing a purple card is ____%
greater than the theoretical probability.

Answer 1

Answer: Below :)

Explanation:

Part A:

The theoretical probability of drawing a purple card from the hat is the number of purple cards divided by the total number of cards in the hat:

P(purple) = 14 / (12 + 17 + 14 + 7) = 14 / 50 = 0.28

So the theoretical probability of drawing a purple card is 0.28 or 28%.

Part B:

The theoretical probability of drawing a purple card is 0.28.

The experimental probability of drawing a purple card is the number of times a purple card was drawn divided by the total number of draws:

Experimental probability = 324 / 1080 = 0.3

To find how much greater the experimental probability is than the theoretical probability, we can calculate the difference and express it as a percentage:

Difference = Experimental probability - Theoretical probability

Difference = 0.3 - 0.28 = 0.02

Percentage greater = (Difference / Theoretical probability) x 100%

Percentage greater = (0.02 / 0.28) x 100% = 7.14%

So the experimental probability is 7.14% greater than the theoretical probability.