I/GCSE Mathematics Question Analysis Topic: Mathematics - Probability
A die is thrown. Let 'A' be the event that the number obtained is greater than 3. Let 'B' be the event that the number obtained is less than 5. Then, P(A∪B) is
(A) 1
(B) 2/5
(C) 3/5
(D) 0
Answer:
For I/GCSE Mathematics, you should know:
When the dice is thrown,
S = {1, 2, 3, 4, 5, 6} i.e. n(S) = 6.
Let A be the scenario where the number gotten is more than 3. i.e. A = {4, 5, 6} => n(A) = 3 => P(A) = n(A) / n(S) = 3/6 = 1/2.
Let B be the scenario where the number gotten is less than 5.
i.e. B = {1, 2, 3, 4} = n(B) = 4 => P(B) = n(B) / n(S) = 4/6 = 2/3.
A∩B = {4} => n(A∩B) = 1
=> P(A∩B) = n(A∩B) / (n(S) = 1/6
P(A∪B) = P(A) + P(B) - P(A∩B)
= 1/2 + 2/3 - 1/6
= (3 + 4 - 1) / 6 = 6/6 = 1
Therefore, P(A∪B) = 1
Work hard for your I/GCSE Mathematics examination!
End of analysis. Great!
