A bag contains 8 red and 7 black balls. Two balls are drawn at random. probability that both balls a

English

Gujarati

Hindi

14.Probability

easy

A bag contains $8$ red and $7$ black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is

A

$\frac{{14}}{{15}}$

B

$\frac{{11}}{{15}}$

C

$\frac{7}{{15}}$

D

$\frac{4}{{15}}$

Solution

(c) Required probability

$=$ Either the balls are red or the balls are black

$ = \frac{{^8{C_2}}}{{^{15}{C_2}}} + \frac{{^7{C_2}}}{{^{15}{C_2}}} = \frac{{28 + 21}}{{105}}$$ = \frac{{49}}{{105}} = \frac{7}{{15}}$.

Standard 11

Mathematics

Share

Similar Questions

Find the probability that when a hand of $7$ cards is drawn from a well shuffled deck of $52$ cards, it contains $3$ Kings.

medium

A box contains $24$ identical balls, of which $12$ are white and $12$ are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the $4^{th}$ time on the $7^{th}$ draw is

easy

(IIT-1994)

In a relay race there are five teams $A, \,B, \,C, \,D$ and $E$. What is the probability that $A,\, B$ and $C$ are first three to finish (in any order) (Assume that all finishing orders are equally likely)

medium

The probability that two randomly selected subsets of the set $\{1,2,3,4,5\}$ have exactly two elements in their intersection, is :

medium

(JEE MAIN-2021)

Twenty tickets are marked the numbers $1, 2, ….. 20.$ If three tickets be drawn at random, then what is the probability that those marked $7$ and $11$ are among them

easy