Multiple choice

A box contains x red balls, y yellow balls and 5 black balls and the number of red balls is 50% more than yellow balls in that box. If the probability of drawn a yellow balls in the box is 4/15, then find the total number of balls in the box?

  1. 30

  2. 15

  3. 21

  4. 45

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Red = 1.5 * Yellow. Let Yellow = y, Red = 1.5y, Black = 5. Total = 2.5y + 5. P(Yellow) = y / (2.5y + 5) = 4/15. 15y = 10y + 20, so 5y = 20, y = 4. Red = 6. Total = 4 + 6 + 5 = 15.

AI explanation

Let the number of yellow balls be y, so the number of red balls x is 1.5y. The total number of balls is the sum of red, yellow and black balls, which is 1.5y plus y plus 5, equaling 2.5y plus 5. Using the given probability of drawing a yellow ball, y divided by 2.5y plus 5 equals 4 divided by 15. Solving this equation yields y equals 4, meaning the total number of balls is 2.5 times 4 plus 5, which is 15.

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