Find the probability that the month of February.

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Find the probability that the month of February may have 5 Wednesdays in
(i) a leap year
(ii) a non-leap year.

Solution:

In the month of February, there are 29 days in a leap year
while 28 days in a non-leap year,
(i) In a leap year, there are 4 complete weeks and 1 day
Probability of Wednesday = P (E) = \\ \frac { 1 }{ 7 }
(ii) and in a non leap year, there are 4 complete weeks and 0 days
Probability of Wednesday P (E) = \\ \frac { 0 }{ 7 } = 0

Sixteen cards are labelled 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:

Here, sample space (S) = {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p)
∴n(S) = 16
(i) Vowels (V) = {a, e, i, o}
∴n(V) = 4
∴P(a vowel) = \\ \frac { n(V) }{ n(S) } = \\ \frac { 4 }{ 16 } = \\ \frac { 1 }{ 4 }
(ii) Consonants (C) = {b, c, d, f, g, h, j, k, l, m, n, p}
∴n(C) = 12
∴P (a consonant) = \\ \frac { n(C) }{ n(S) } = \\ \frac { 12 }{ 16 } = \\ \frac { 3 }{ 4 }
(iii) None of the letters of the word MEDIAN (N) = {b, c, f, g, h, j, k, l, o, p)
∴n(N) = 10
∴P (N) = \\ \frac { n(N) }{ n(S) } = \\ \frac { 10 }{ 16 } = \\ \frac { 5 }{ 8 }

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