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Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
- a)1/2
- b)3/4
- c)3/8
- d)5/16
Correct answer is option 'B'. Can you explain this answer?
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Two dice are thrown simultaneously. What is the probability of getting...
In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.
Then, E = ((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)}
Then, E = ((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)}
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Two dice are thrown simultaneously. What is the probability of getting...
Understanding the Problem:
When two dice are thrown simultaneously, each dice has 6 possible outcomes (numbers 1 to 6). To find the probability of getting two numbers whose product is even, we need to consider the possible outcomes where at least one of the numbers is even.
Calculating the Total Number of Outcomes:
Since each dice has 6 possible outcomes, the total number of outcomes when two dice are thrown simultaneously is 6 * 6 = 36.
Calculating the Number of Favorable Outcomes:
To find the favorable outcomes where the product is even, we consider the following cases:
1. The first number is even and the second number can be any (3 possibilities).
2. The first number is odd and the second number is even (3 possibilities).
3. Both numbers are even (3 possibilities).
Therefore, the total number of favorable outcomes is 3 + 3 + 3 = 9.
Calculating the Probability:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
Probability = 9 / 36
Probability = 1/4
Probability = 3/4
Therefore, the probability of getting two numbers whose product is even is 3/4, which corresponds to option 'B'.
When two dice are thrown simultaneously, each dice has 6 possible outcomes (numbers 1 to 6). To find the probability of getting two numbers whose product is even, we need to consider the possible outcomes where at least one of the numbers is even.
Calculating the Total Number of Outcomes:
Since each dice has 6 possible outcomes, the total number of outcomes when two dice are thrown simultaneously is 6 * 6 = 36.
Calculating the Number of Favorable Outcomes:
To find the favorable outcomes where the product is even, we consider the following cases:
1. The first number is even and the second number can be any (3 possibilities).
2. The first number is odd and the second number is even (3 possibilities).
3. Both numbers are even (3 possibilities).
Therefore, the total number of favorable outcomes is 3 + 3 + 3 = 9.
Calculating the Probability:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
Probability = 9 / 36
Probability = 1/4
Probability = 3/4
Therefore, the probability of getting two numbers whose product is even is 3/4, which corresponds to option 'B'.
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Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?a)1/2b)3/4c)3/8d)5/16Correct answer is option 'B'. Can you explain this answer?
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