A bag contains 2 Red, 3 Green and 2 Blue ball. 2 balls are to be drawn randomly. What is the probability that the balls drawn contain no blue ball?

To solve this problem, we need to understand the basics of probability and combinations.

Step 1: Calculate the total number of balls The bag contains 2 Red, 3 Green, and 2 Blue balls. So, the total number of balls is 2 + 3 + 2 = 7 balls.

Step 2: Calculate the total number of ways to draw 2 balls from 7 The number of ways to draw 2 balls from 7 (without considering the color of the balls) can be calculated using the combination formula C(n, r) = n! / [(n-r)! * r!], where n is the total number of items, and r is the number of items to choose. So, C(7, 2) = 7! / [(7-2)! * 2!] = 21 ways.

Step 3: Calculate the number of ways to draw 2 balls with no blue We have 5 balls that are not blue (2 Red and 3 Green). The number of ways to draw 2 balls from these 5 can be calculated as C(5, 2) = 5! / [(5-2)! * 2!] = 10 ways.

Step 4: Calculate the probability The probability of an event is the number of favorable outcomes divided by the total number of outcomes. So, the probability that the balls drawn contain no blue ball is 10 / 21 = 0.4762 or 47.62% when expressed as a percentage.