What is the probability that it is a vowel.

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A letter is chosen from the word ‘TRIANGLE’. What is the probability that it is a vowel?

Solution:

There are three vowels: I, A, E
.’. The number of letters in the word ‘TRIANGLE’ = 8.
Probability of vowel
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 3 }{ 8 }

A letter of English alphabet is chosen at random. Determine the probability that the letter is a consonant.

Solution:

No. of English alphabet = 26
No. of vowel = 5
No. of constant = 25 – 5 = 21
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 21 }{ 26 }

A bag contains 5 black, 7 red and 3 white balls. A ball is drawn at random from the bag, find the probability that the ball drawn is:
(i) red
(ii) black or white
(iii) not black.

Solution:

In a bag,
Number of black balls = 5
Number of red balls = 7
and number of white balls = 3
Total number of balls in the bag
= 5 + 7 + 3 = 15
(i) Probability of red balls
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 7 }{ 15 }
(ii) Probability of black or white balls
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 5+3 }{ 15 }
= \\ \frac { 8 }{ 15 }
(iii) Probability of not black balls
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 7+3 }{ 15 }
= \\ \frac { 10 }{ 15 }
= \\ \frac { 2 }{ 3 }

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