**Question:**

A jar contains 6 red buttons and 10 black buttons. If two buttons are picked at random and without replacement, what is the probability of picking two buttons of different colour?

**Answer-1**

You can pick two buttons of different color if there are two colors in two different ways: 1. you first pick a red one, then a black one. 2. you first pick a black one, then a red one.

let's consider case number 1:

the probability of 1. happening is the probability of picking a red button (6 out of 16, or 6/16) times the probability of picking a black button given one red button has been already picked (10/15). 6/16*10/15 = 1/4

the probability of 2. happening:

10/16 * 6/15 = 1/4

since you don;t care about the order, 1. and 2. are fine. therefore you sum up the respective probabilities. 1/4 + 1/4 = 1/2

let's consider case number 1:

the probability of 1. happening is the probability of picking a red button (6 out of 16, or 6/16) times the probability of picking a black button given one red button has been already picked (10/15). 6/16*10/15 = 1/4

the probability of 2. happening:

10/16 * 6/15 = 1/4

since you don;t care about the order, 1. and 2. are fine. therefore you sum up the respective probabilities. 1/4 + 1/4 = 1/2

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