Question

Suppose we throw a die once.
(i) What is the probability of getting a number greater than 4?
(ii) What is the probability of getting a number less than or equal to 4?

Answer 1

S = {1,2,3,4,5,6}; n(S)=6
(i)
A = {5,6}; n(A)=2
P(A) = n(A)/n(S) = 2/6 = 1/3

(ii)
B={1,2,3,4}; n(B)=4
P(B) = n(B)/n(S) = 4/6 = 2/3

Answer 2

(i) The probability of getting a number greater than 4 is $\dfrac{1}{3}$

(ii) The probability of getting a number less than or equal to 4 is $\dfrac{2}{3}$

Step-by-step explanation:

Throwing a dice there are six possible outcomes

S={1,2,3,4,5,6}

$\left | \textrm{S} \right |=6$

Let A be the event of getting number greater than 4

A={5,6}  

so $\left | \textrm{A} \right |=2$

P(getting number greater than 4) = $\textrm P(\textrm {A})=\frac{\left | \textrm{A} \right |}{\left | \textrm{S}} \right |}=\frac{2}{6} =\frac{1}{3}$

Let B be the event of getting number less than or equal to 4

B={1,2,3,4}

So $\left | \textrm{B} \right |=4$

P(getting number less than or equal to 4)=$\textrm P(\textrm{B})=\frac{\left | \textrm{B} \right |}{\left | \textrm{S}} \right |}=\frac{4}{6}=\frac{2}{3}$