**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

About Us
Gradeup Exam Prep
News
Blog
Contact Us
Terms and Conditions
mail us at [email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */