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Two dice are thrown. Find the probability that the product of two numbers received is even.
- a)3/4
- b)1/2
- c)1
- d)1/4
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two dice are thrown. Find the probability that the product of two num...
Probability = 1 - Both off numbers / Total cases
Total cases = 62
Both odd numbers
= 
Probability = 
= 3/4
Most Upvoted Answer
Two dice are thrown. Find the probability that the product of two num...
Probability = 1 - Both off numbers / Total cases
Total cases = 62
Both odd numbers
=
Probability =
= 3/4
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Community Answer
Two dice are thrown. Find the probability that the product of two num...
Understanding the Problem
When two dice are thrown, each die has 6 faces numbered from 1 to 6. We want to find the probability that the product of the two numbers obtained is even.
Possible Outcomes
- Each die can land on any of its 6 faces.
- Therefore, the total number of outcomes when two dice are thrown is:
- Total outcomes = 6 (from die 1) x 6 (from die 2) = 36.
When is the Product Even?
- The product of two numbers is even if at least one of the numbers is even.
- The even numbers on a die are: 2, 4, and 6.
- The odd numbers on a die are: 1, 3, and 5.
Calculating Odd Outcomes
- For the product to be odd, both numbers must be odd.
- The odd numbers available are 1, 3, and 5 (3 options).
- The combinations for odd outcomes:
- Odd outcomes = 3 (from die 1) x 3 (from die 2) = 9.
Calculating Even Outcomes
- To find the even outcomes:
- Even outcomes = Total outcomes - Odd outcomes
- Even outcomes = 36 - 9 = 27.
Calculating Probability
- The probability that the product is even is given by:
- Probability = Even outcomes / Total outcomes
- Probability = 27 / 36 = 3 / 4.
Conclusion
Thus, the probability that the product of the two numbers received is even is 3/4, which corresponds to option 'A'.
When two dice are thrown, each die has 6 faces numbered from 1 to 6. We want to find the probability that the product of the two numbers obtained is even.
Possible Outcomes
- Each die can land on any of its 6 faces.
- Therefore, the total number of outcomes when two dice are thrown is:
- Total outcomes = 6 (from die 1) x 6 (from die 2) = 36.
When is the Product Even?
- The product of two numbers is even if at least one of the numbers is even.
- The even numbers on a die are: 2, 4, and 6.
- The odd numbers on a die are: 1, 3, and 5.
Calculating Odd Outcomes
- For the product to be odd, both numbers must be odd.
- The odd numbers available are 1, 3, and 5 (3 options).
- The combinations for odd outcomes:
- Odd outcomes = 3 (from die 1) x 3 (from die 2) = 9.
Calculating Even Outcomes
- To find the even outcomes:
- Even outcomes = Total outcomes - Odd outcomes
- Even outcomes = 36 - 9 = 27.
Calculating Probability
- The probability that the product is even is given by:
- Probability = Even outcomes / Total outcomes
- Probability = 27 / 36 = 3 / 4.
Conclusion
Thus, the probability that the product of the two numbers received is even is 3/4, which corresponds to option 'A'.
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Two dice are thrown. Find the probability that the product of two numbers received is even.a)3/4b)1/2c)1d)1/4Correct answer is option 'A'. Can you explain this answer?
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