Determine the probability p, for each of the following events.
(a) An odd number appears in a single toss of a fair die.
(b) At least one head appears in two tosses of a fair coin.
(c) A king, 9 of hearts, or 3 of spades appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
(d) The sum of 6 appears in a single toss of a pair of fair dice.
(a) When a fair die is thrown, the possible outcomes are $S=\{1,2,3,4,5,6\}$
$\therefore$ total outcomes $=6$ and the odd numbers are $1,3,5$
$\therefore$ Favourable outcomes $=3$
We know that,
Probability $=\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}$
$\therefore$ Required probability $=\frac{3}{6}=\frac{1}{2}$
(b) When a fair coin is tossed two times, the sample space is $\mathrm{S}=\{\mathrm{HH}, \mathrm{HT}, \mathrm{TH}, \mathrm{TT}\}$
$\therefore$ Total outcomes $=4$
If at least one head appears then the favourable cases are $\mathrm{HH}, \mathrm{HT}$ and $\mathrm{TH}$.
$\therefore$ Favourable outcomes $=3$
We know that,
Probability $=\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}$
$\therefore$ Required probability $=\frac{3}{4}$
(c) When a pair of dice is rolled, total number of cases
S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
Total Sample Space, n(S) = 36
If sum is 6 then possible outcomes are (1,5), (2,4), (3,3), (4,2) and (5,1).
∴ Favourable outcomes = 5
We know that,
Probability $=\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}$
$\therefore$ Required probability $=\frac{5}{36}$
objective TYPE questions: