Question

A bag contains marbles of four different colors: 8 blue marbles 24 red marbles 16 green marbles 4 yellow marbles Which statement(s) accurately determines the probability of picking a yellow marble at random from the bag? Select ALL that apply. Responses Find the sum of the probabilities of picking red, green, and blue, and subtract that value from 1 . Find the sum of the probabilities of picking red, green, and blue, and subtract that value from 1. Divide the number of yellow marbles by the sum of the red, green, and blue marbles. Divide the number of yellow marbles by the sum of the red, green, and blue marbles., Divide the number of yellow marbles by the sum of the red, green, blue, and yellow marbles. Divide the number of yellow marbles by the sum of the red, green, blue, and yellow marbles., Find the total number of marbles, and divide this by the number of yellow marbles. Find the total number of marbles, and divide this by the number of yellow marbles., Find the sum of the red, green, and blue marbles, and divide this by the number of yellow marbles. Find the sum of the red, green, and blue marbles, and divide this by the number of yellow marbles.,

Answer 1

Explanation:

Here's a step-by-step explanation of each statement:

1. Find the sum of the probabilities of picking red, green, and blue, and subtract that value from 1.

Calculate the probability of picking each color:

P(red) = 24/(8+24+16+4) = 24/52

P(green) = 16/52

P(blue) = 8/52

Sum the probabilities: P(red) + P(green) + P(blue) = 24/52 + 16/52 + 8/52 = 48/52

Subtract the sum from 1: 1 - 48/52 = 4/52

This method is correct.

• Divide the number of yellow marbles by the sum of the red, green, and blue marbles.

This method incorrectly ignores the yellow marbles in the denominator. Therefore, it is not correct.

• Divide the number of yellow marbles by the sum of the red, green, blue, and yellow marbles.

This is the standard method for calculating probabilities: P(yellow) = 4/(8+24+16+4) = 4/52

This method is correct.

• Find the total number of marbles, and divide this by the number of yellow marbles.

This method reverses the numerator and denominator, so it is not correct.

• Find the sum of the red, green, and blue marbles, and divide this by the number of yellow marbles.

This method also reverses the numerator and denominator, so it is not correct.

In summary, the correct statements are:

1. Find the sum of the probabilities of picking red, green, and blue, and subtract that value from 1.
2. Divide the number of yellow marbles by the sum of the red, green, blue, and yellow marbles.