Sixteen cards are labeled as a, b, c,…, m, n, o, p. They are put in a box and shuffled. A boy is asked to draw a card from the box. What is the probability that the card drawn is:
(i) a vowel
(ii) a consonant
(iii) none of the letters of the word median.

Solution:

The possible outcomes are {a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p}

Number of possible outcomes = 16

(i) Let E be the event of getting a vowel.

Outcomes favourable to E are { a,e,i,o}

Number of favourable outcomes = 4

P(E) = 4/16 = 1/4

Hence the probability of getting a vowel is ¼.

(ii) Let E be the event of getting a consonant.

Outcomes favourable to E are {b,c,d,f,g,h,j,k,l,m,n,p}

Number of favourable outcomes = 12

P(E) = 12/16 = 3/4

Hence the probability of getting a consonant is 3/4.

(iii) Let E be the event of getting none of the letters of word median.

Outcomes favourable to E are {b,c,f,g,h,j,k,l,o,p}

Number of favourable outcomes = 10

P(E) = 10/16 = 5/8

Hence the probability of getting none of the letters of word median is 5/8.