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Two dice are thrown together. Find the probability of getting a multiple of 2 on one dice and multiple of 3 on the other.
- a)2/3
- b)1/6
- c)1/3
- d)None of the above.
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Two dice are thrown together. Find the probability of getting a multip...
Probability of getting a multiple of 2 on one dice and multiple of 3 on the other
To solve this problem, we need to first determine the total number of possible outcomes when two dice are thrown together. Each dice has 6 possible outcomes, so the total number of outcomes is 6 x 6 = 36.
Next, we need to determine the number of outcomes where one dice shows a multiple of 2 and the other dice shows a multiple of 3.
- Multiples of 2: 2, 4, 6
- Multiples of 3: 3, 6
We can see that the only common multiple is 6. So, we need to find the number of outcomes where one dice shows 2 or 4 or 6 and the other dice shows 3 or 6.
- Dice 1 shows 2 and dice 2 shows 3 or 6: 1 x 2 = 2 outcomes
- Dice 1 shows 4 and dice 2 shows 3 or 6: 1 x 2 = 2 outcomes
- Dice 1 shows 6 and dice 2 shows 3 or 6: 1 x 2 = 2 outcomes
Therefore, the total number of outcomes where one dice shows a multiple of 2 and the other dice shows a multiple of 3 is 2 + 2 + 2 = 6.
The probability of getting a multiple of 2 on one dice and multiple of 3 on the other is the ratio of favorable outcomes to total outcomes.
- Probability = favorable outcomes / total outcomes
- Probability = 6 / 36
- Probability = 1 / 6
Therefore, the correct answer is option B) 1/6.
To solve this problem, we need to first determine the total number of possible outcomes when two dice are thrown together. Each dice has 6 possible outcomes, so the total number of outcomes is 6 x 6 = 36.
Next, we need to determine the number of outcomes where one dice shows a multiple of 2 and the other dice shows a multiple of 3.
- Multiples of 2: 2, 4, 6
- Multiples of 3: 3, 6
We can see that the only common multiple is 6. So, we need to find the number of outcomes where one dice shows 2 or 4 or 6 and the other dice shows 3 or 6.
- Dice 1 shows 2 and dice 2 shows 3 or 6: 1 x 2 = 2 outcomes
- Dice 1 shows 4 and dice 2 shows 3 or 6: 1 x 2 = 2 outcomes
- Dice 1 shows 6 and dice 2 shows 3 or 6: 1 x 2 = 2 outcomes
Therefore, the total number of outcomes where one dice shows a multiple of 2 and the other dice shows a multiple of 3 is 2 + 2 + 2 = 6.
The probability of getting a multiple of 2 on one dice and multiple of 3 on the other is the ratio of favorable outcomes to total outcomes.
- Probability = favorable outcomes / total outcomes
- Probability = 6 / 36
- Probability = 1 / 6
Therefore, the correct answer is option B) 1/6.
Community Answer
Two dice are thrown together. Find the probability of getting a multip...
A and B are independent events.
P(A intersection B) = P(A).P(B)
= (1/2)(1/3) = 1/6.
P(A intersection B) = P(A).P(B)
= (1/2)(1/3) = 1/6.
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Two dice are thrown together. Find the probability of getting a multiple of 2 on one dice and multiple of 3 on the other.a)2/3b)1/6c)1/3d)None of the above.Correct answer is option 'B'. Can you explain this answer?
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