Question

. A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. If one ball is drawn at random. Find the probability that it is
(a) Black (b) red (c) not green

Answer 1

AnswEr:

• Red Balls = 5

• White Balls = 8

• Green Balls = 4

• Black Balls = 7

Total Number of Balls = 5 + 8 + 7 + 4

$:\implies\sf\: 24$

$\rule{150}2$

We know that,

$:\implies\small{\underline{\boxed{\sf{\red{\dfrac{Number\:of\: Favourable\; Outcomes}{Total\: Number\:of\: Outcomes}}}}}}$

a) Number of Black Balls

Total Number of Balls = 24

Number of Black Balls = 7

$:\implies\sf\: \dfrac{7}{24}$

$\rule{150}2$

b) Red

Total Number of Balls = 24

Number of Red Balls = 5

$:\implies\sf\dfrac{5}{24}$

$\rule{150}2$

c) Numbers of Balls Which are not Green

$:\implies\sf\: 5 + 8 + 7$

$:\implies\sf\: 20$

$:\implies\sf\dfrac{20}{24}$

$:\implies\sf\dfrac{5}{6}$

Answer 2

$\huge \underline {\underline{ \mathfrak{ \green{AnS}wEr \colon}}}$

Given :

• Red Balls = 5
• White Balls = 8
• Green Balls = 4
• Black Balls = 7

$\rule{150}{0.5}$

To Find :

The probability that it is :

1. Black
2. Red
3. Not green

$\rule{150}{0.5}$

Solution :

Total No. of Balls = 5 + 7 + 4 + 8 = 24

We have formula for Probability :

$\bigstar \: {\boxed{\sf{Probability \: = \: \dfrac{No. \: of \: Favourable \: Outcome}{Total \: no. \: of \: outcomes}}}}$

______________________

$\underline{\bf{(1) \: Probability \: of \: Black \: Balls}} \\ \\ \\ \: \: \: \: \: \: \bullet \: \sf{Total \: no. \: = \: 24} \\ \\ \: \: \: \: \: \: \bullet \: \sf{No. \: of \: Black Balls \: = \: 7} \\ \\ \\ \implies {\sf{Probability \: = \: \dfrac{7}{24}}} \\ \\ \longrightarrow {\boxed{\sf{Probability \: = \: \dfrac{7}{24}}}}$

$\rule{100}{1}$

$\underline{\bf{(2) \: Probability \: of \: Red \: balls}} \\ \\ \\ \: \: \: \: \: \: \dag \: \sf{Total \: no. \: of \: balls \: = \: 24} \\ \\ \: \: \: \: \: \: \dag \: \sf{No. \: of \: red \: balls \: = \: 5} \\ \\ \\ \implies {\sf{Probability \: = \: \dfrac{5}{24}}} \\ \\ \longrightarrow {\boxed{\sf{Probability \: = \: \dfrac{5}{24}}}}$

$\rule{100}{1}$

$\underline{\bf{(3) \: Probability \: of \: not \: green \: balls}} \\ \\ \\ \: \: \: \: \: \: \ddag \: \sf{No. \: of \: Balls \: = \: 24} \\ \: \: \: \: \: \: \ddag \: \sf{No. \: of \: Not \: green \: balls \: = \: 20} \\ \\ \\ \implies {\sf{Probability \: = \: \dfrac{20}{24}}} \\ \\ \implies {\sf{Probability \: = \: \dfrac{5}{6}}} \\ \\ \longrightarrow {\boxed{\sf{Probability \: = \: \dfrac{5}{6}}}}$