A die is thrown find the probability of following events:
(i) A prime number will appear
(ii) A number greater than or equal to $3$ will appear
(iii) A number less than or equal to one will appear
(iv) A number more than $6$ will appear
(v) A number less than $6$ will appear

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Solution

The sample space of the given experiment is given by,
$S = {1, 2, 3, 4, 5, 6}$
(i) Let $A$ be the event of the occurrence of a prime number $\Rightarrow A = {2, 3, 5}$
$∴ P (A) = \frac{N u m b e r o f o u t c o m e s f a v o u r a b l e t o A}{T o t a l n u m b e r o f p o s s i b l e o u t c o m e s} = \frac{n (A)}{n (S)} = \frac{3}{6} = \frac{1}{2}$
(ii) Let $B$ be the event of the occurrence of a number greater than or equal to $3$ $\Rightarrow B = {3, 4, 5, 6}$
$∴ P (B) = \frac{N u m b e r o f o u t c o m e s f a v o u r a b l e t o B}{T o t a l n u m b e r o f p o s s i b l e o u t c o m e s} = \frac{n (B)}{n (S)} = \frac{4}{6} = \frac{2}{3}$
(iii) Let $C$ be the event of the occurrence of a number less than or equal to one $\Rightarrow C = {1}$
$∴ P (C) = \frac{N u m b e r o f o u t c o m e s f a v o u r a b l e t o C}{T o t a l n u m b e r o f p o s s i b l e o u t c o m e s} = \frac{n (C)}{n (S)} = \frac{1}{6}$
(iv) Let $D$ be the event of the occurrence of a number greater than $6$ $\Rightarrow D = ϕ$
$∴ P (D) = \frac{N u m b e r o f o u t c o m e s f a v o u r a b l e t o D}{T o t a l n u m b e r o f p o s s i b l e o u t c o m e s} = \frac{n (D)}{n (S)} = \frac{0}{6} = 0$
(v) Let $E$ be the event of the occurrence of a number less than $6$ $\Rightarrow E = {1, 2, 3, 4, 5}$
$∴ P (E) = \frac{N u m b e r o f o u t c o m e s f a v o u r a b l e t o E}{T o t a l n u m b e r o f p o s s i b l e o u t c o m e s} = \frac{n (E)}{n (S)} = \frac{5}{6}$

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Similar questions

A die is thrown, find the probability of following events:

(i) A prime number will appear,

(ii) A number greater than or equal to 3 will appear,

(iii) A number less than or equal to one will appear,

(iv) A number more than 6 will appear,

(v) A number less than 6 will appear.

A die is thrown, find the probability of follwoing events:
(i) A prime number will appear.
(ii) A number greater than or equal to 3 will appear
(iii) A numbher less than or equal to one will appar.
(iv) A number more than 6 will appear.
(v) A number less tahn 6 will appear.

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