How to Solve Probability using Picture?

The Probability and data arrangement Math is generally related to understand different ways of managing data. Probability or likelihood of certain event can be mutually independent or mutually dependent. We can evaluate the probability of the events with help of pictures also. So, let us see how to solve probability using picture.

Example: 



Find the probability of getting 4 balls of the same colour?

Solution: As we can see in the figure it is given that a bag contains 10 black, 10 blue and 10 white balls. We have to find the probability of getting 4 balls of the same colour. 1st of all we need to evaluate the Sample Space for the probability: the total number of balls in the bag is 10 + 10 + 10 = 30 and for choosing 4 balls out of 30 we would write the possible cases as: ³⁰ C ₄. Next we evaluate the condition which says the 4 balls should be of the same colour and the possibilities are either 4 black, 4 blue or 4 white balls. The total number of possible ways for doing it is:

¹⁰C ₄ + ¹⁰ C ₄ + ¹⁰ C ₄,

To Calculate The Probability we divide the probable cases by the same space. So, the probability of getting 4 balls of the same color will be:(¹⁰ C ₄ + ¹⁰ C ₄ + ¹⁰ C ₄) / ³⁰ C ₄

Or 3 (10 * 9 * 8 * 7 / 4 * 3 * 2 * 1) / (30 * 29 * 28 * 27 / 4 * 3 * 2 * 1),

Or 3 (10 * 9 * 8 * 7) / (30 * 29 * 28 * 27) = 2 / (3 * 29) = 2 /87 .