Question

A bag contains a total of 116 red, white, blue, and yellow marbles. The red marbles are numbered 1 through 29,

he white marbles are numbered 1 through 29, and so on. One marble is randomly selected from the bag.
Determine the probability of selecting a yellow marble or a number less than 6. Record the answer as a fraction.

Answer 1

Answer: 39/116

Explanation:

To find the probability of selecting a yellow marble or a number less than 6, we need to count the total number of favorable outcomes and divide it by the total number of possible outcomes.

Let's break down the information given:

There are 29 red marbles.

There are 29 white marbles.

There are 29 blue marbles.

There are 29 yellow marbles.

The total number of marbles is 29 + 29 + 29 + 29 = 116

Now, for the numbers less than 6, we have the following possibilities:

Red marbles with numbers 1 through 5: 5 marbles

White marbles with numbers 1 through 5: 5 marbles

Blue marbles with numbers 1 through 5: 5 marbles

The total number of marbles with numbers less than 6 is 5 + 5 + 5 = 15.

However, we need to be careful not to double-count the yellow marbles with numbers less than 6. Since we've already counted the yellow marbles with numbers 1 through 5 in the previous count, we need to subtract the yellow marbles with numbers 1 through 5 (5 marbles) from the total.

So, the total number of marbles with numbers less than 6, excluding yellow marbles with numbers 1 through 5, is 15 − 5 = 10.

Now, the total number of favorable outcomes (selecting a yellow marble or a number less than 6) is 29 + 10 = 39.

The probability is given by the ratio of favorable outcomes to total outcomes:

P= (Total Number of Outcomes)/(Number of Favorable Outcomes)

P= (116)/(39)

So, the probability of selecting a yellow marble or a number less than 6 is

39/116.