Question

QNO 2. Each of the letter of the word EXCELLENCE is printed on a
separate card and the card are put into a box.Two cards are drawn at
random from the box,one at a time,without replacement.Find the
probability that
i)both cards contain vowels

ii)the first card drawn contains a vowel

iii)the letter on two cards are same

Answer 1

Given:

Each of the letter of the word EXCELLENCE is printed on a

separate card and the card are put into a box.

To find:

probability that

i)both cards contain vowels

ii)the first card drawn contains a vowel

iii)the letter on two cards are same

Solution:

1) The number of the Letter in EXCELLENCE is 10 = P(E)

• Vowels is 4

2) both cards contain vowels = Number of the favorable outcome/ total number of the outcome.

• P = 4/10×3/9

P =2/15

3) the first card drawn contains a vowel = Number of the favorable outcome/ total number of the outcome.

• P = 4/10×6/9

P = 4/15

4)the letter on two cards are same= Number of the favorable outcome/ total number of the outcome.

• P = 4/10×3/9 + 2/10×1/9 + 2/10×1/9

• P = 2/15 + 1/45 + 1/45

P = 8/45