Question:
Two dice are thrown simultaneously. The probability of getting two numbers whose product is even is:
Two dice are thrown simultaneously. The probability of getting two numbers whose product is even is:
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For probability questions involving “even product”, it is usually easier to first calculate the probability of getting an odd product and then subtract from \(1\).
Updated On: Jun 24, 2026
- \(\dfrac{1}{2}\)
- \(\dfrac{3}{4}\)
- \(\dfrac{3}{8}\)
- \(\dfrac{5}{16}\)
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The Correct Option is B
Solution and Explanation
Step 1: Find the total number of outcomes.
When two dice are thrown simultaneously, \[ \text{Total outcomes}=6\times 6=36 \]
Step 2: Use the complement method.
The product of two numbers is even unless both numbers are odd.
Odd numbers on a die are \[ 1,\ 3,\ 5 \] Thus, probability of getting an odd number on one die is \[ \frac{3}{6}=\frac{1}{2} \] Therefore, probability that both dice show odd numbers is \[ \frac{1}{2}\times \frac{1}{2} = \frac{1}{4} \]
Step 3: Find the required probability.
Required probability \[ =1-\frac{1}{4} \] \[ =\frac{3}{4} \]
Step 4: Final conclusion.
Hence, \[ \boxed{\frac{3}{4}} \]
When two dice are thrown simultaneously, \[ \text{Total outcomes}=6\times 6=36 \]
Step 2: Use the complement method.
The product of two numbers is even unless both numbers are odd.
Odd numbers on a die are \[ 1,\ 3,\ 5 \] Thus, probability of getting an odd number on one die is \[ \frac{3}{6}=\frac{1}{2} \] Therefore, probability that both dice show odd numbers is \[ \frac{1}{2}\times \frac{1}{2} = \frac{1}{4} \]
Step 3: Find the required probability.
Required probability \[ =1-\frac{1}{4} \] \[ =\frac{3}{4} \]
Step 4: Final conclusion.
Hence, \[ \boxed{\frac{3}{4}} \]
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