Question
Two dice are rolled together. What is the probability of getting two numbers whose product is even?
Two dice are rolled together. What is the probability of getting two numbers whose product is even?
Answer: Option C
----------------------------------------------------------------------------------------- This problem can easily be solved if we know the following property of numbers
)
$MF#%= \dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}$MF#%
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Answer : Option C
Explanation :
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Solution 1
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Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)
Hence, Total number of outcomes possible when two dice are rolled, n(S) = 6 × 6 = 36
Let E = the event of getting two numbers whose product is even
= {(1,2), (1,4), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6),
(3,2), (3,4), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6),
(5,2),(5,4), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
Hence, n(E) = 27
$MF#%\text{P(E) = }\dfrac{\text{n(E)}}{\text{n(S)}} = \dfrac{27}{36} = \dfrac{3}{4}$MF#%
----------------------------------------------------------------------------------------- Solution 2----------------------------------------------------------------------------------------- This problem can easily be solved if we know the following property of numbers
)
$MF#%= \dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}$MF#%
$MF#%\text{P(Even product) = 1 - P(Odd product) = }1 - \dfrac{1}{4} = \dfrac{3}{4}$MF#%
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