Question

A glass Jar contains 8 blue, 5 red, 4 yellow and 3 green marbles. A single marble is drawn at random from the Jar What is the probability of choosing (i) a green marble? (ii) a blue marble? (iii) a yellow marble? (iv) a red marble?​

Answer 1

GiveN:-

A glass Jar contains 8 blue, 5 red, 4 yellow and 3 green marbles. A single marble is drawn at random from the Jar.

To FinD:-

What is the probability of choosing (i) a green marble? (ii) a blue marble? (iii) a yellow marble? (iv) a red marble?

SolutioN:-

We know that,

$\large{\green{\underline{\boxed{\bf{P(E)=\dfrac{No.\:of\:Favourable\:Outcomes}{Total\:no\:of\:possible\:Outcomes}}}}}}$

(i) A Green Marble:-

• Total outcomes = 8 + 5 + 4 + 3 = 20
• Favourable Outcomes = 3

So,

$\large\implies{\sf{P_{(green\:marble)}=\dfrac{No.\:of\:Favourable\:Outcomes}{Total\:no\:of\:possible\:Outcomes}}}$

$\large\implies{\sf{P_{(green\:marble)}=\dfrac{3}{20}}}$

Probability of getting green marble is 3/20

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(ii) A Blue Marble:-

• Total outcomes = 8 + 5 + 4 + 3 = 20
• Favourable Outcomes = 8

So,

$\large\implies{\sf{P_{(blue\:marble)}=\dfrac{No.\:of\:Favourable\:Outcomes}{Total\:no\:of\:possible\:Outcomes}}}$

$\large\implies{\sf{P_{(blue\:marble)}=\dfrac{8}{20}}}$

$\large\implies{\sf{P_{(blue\:marble)}=\dfrac{\cancel{8}}{\cancel{20}}}}$

$\large\implies{\sf{P_{(blue\:marble)}=\dfrac{2}{5}}}$

Probability of getting blue marble is 2/5.

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(iii) A Yellow Marble:-

• Total outcomes = 8 + 5 + 4 + 3 = 20
• Favourable Outcomes = 4

So,

$\large\implies{\sf{P_{(yellow\:marble)}=\dfrac{No.\:of\:Favourable\:Outcomes}{Total\:no\:of\:possible\:Outcomes}}}$

$\large\implies{\sf{P_{(yellow\:marble)}=\dfrac{4}{20}}}$

$\large\implies{\sf{P_{(yellow\:marble)}=\dfrac{\cancel{4}}{\cancel{20}}}}$

$\large\implies{\sf{P_{(yellow\:marble)}=\dfrac{1}{5}}}$

Probability of getting yellow marble is 1/5.

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(iv) A Red Marble:-

• Total outcomes = 8 + 5 + 4 + 3 = 20
• Favourable Outcomes = 5

So,

$\large\implies{\sf{P_{(red\:marble)}=\dfrac{No.\:of\:Favourable\:Outcomes}{Total\:no\:of\:possible\:Outcomes}}}$

$\large\implies{\sf{P_{(red\:marble)}=\dfrac{5}{20}}}$

$\large\implies{\sf{P_{(red\:marble)}=\dfrac{\cancel{5}}{\cancel{20}}}}$

$\large\implies{\sf{P_{(red\:marble)}=\dfrac{1}{4}}}$

Probability of getting red marble is 1/4.

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