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Two fairdices are thrown. Giventh at the sum of the dice is less than or equal to 4, find the probability that only one dice shows two.
- a)1/4
- b)1/2
- c)2/3
- d)1/3
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Two fairdices are thrown. Giventh at the sum of the dice is less than ...
The possible outcomes are: (1, 1); (1, 2); (2, 1), (2, 2); (3, 1); (1, 3).
Out of six cases, in two cases there is exactly one ‘2’ Thus, the correct answer is 2/6 =1/3.
Out of six cases, in two cases there is exactly one ‘2’ Thus, the correct answer is 2/6 =1/3.
Most Upvoted Answer
Two fairdices are thrown. Giventh at the sum of the dice is less than ...
Solution:
To find the probability that only one dice shows two, we need to consider two scenarios:
1. The first dice shows two and the second dice shows a number less than or equal to 2.
2. The first dice shows a number less than or equal to 2 and the second dice shows two.
Let's calculate the probability for each scenario separately.
Scenario 1: The first dice shows two and the second dice shows a number less than or equal to 2.
The probability of the first dice showing two is 1/6, as there is only one favorable outcome (getting a two) out of six possible outcomes (rolling a fair six-sided dice).
The probability of the second dice showing a number less than or equal to 2 is 2/6, as there are two favorable outcomes (getting a one or a two) out of six possible outcomes.
Using the multiplication rule for independent events, the probability of both events occurring is:
P(First dice shows two and second dice shows a number less than or equal to 2) = P(First dice shows two) * P(Second dice shows a number less than or equal to 2)
= (1/6) * (2/6)
= 1/18
Scenario 2: The first dice shows a number less than or equal to 2 and the second dice shows two.
The probability of the first dice showing a number less than or equal to 2 is 2/6, as there are two favorable outcomes (getting a one or a two) out of six possible outcomes.
The probability of the second dice showing two is 1/6, as there is only one favorable outcome (getting a two) out of six possible outcomes.
Using the multiplication rule for independent events, the probability of both events occurring is:
P(First dice shows a number less than or equal to 2 and second dice shows two) = P(First dice shows a number less than or equal to 2) * P(Second dice shows two)
= (2/6) * (1/6)
= 1/18
Now, to find the probability that only one dice shows two, we need to add the probabilities of both scenarios:
P(Only one dice shows two) = P(First dice shows two and second dice shows a number less than or equal to 2) + P(First dice shows a number less than or equal to 2 and second dice shows two)
= 1/18 + 1/18
= 2/18
= 1/9
Therefore, the probability that only one dice shows two is 1/9, which is not listed as an option. None of the given options match the correct answer.
To find the probability that only one dice shows two, we need to consider two scenarios:
1. The first dice shows two and the second dice shows a number less than or equal to 2.
2. The first dice shows a number less than or equal to 2 and the second dice shows two.
Let's calculate the probability for each scenario separately.
Scenario 1: The first dice shows two and the second dice shows a number less than or equal to 2.
The probability of the first dice showing two is 1/6, as there is only one favorable outcome (getting a two) out of six possible outcomes (rolling a fair six-sided dice).
The probability of the second dice showing a number less than or equal to 2 is 2/6, as there are two favorable outcomes (getting a one or a two) out of six possible outcomes.
Using the multiplication rule for independent events, the probability of both events occurring is:
P(First dice shows two and second dice shows a number less than or equal to 2) = P(First dice shows two) * P(Second dice shows a number less than or equal to 2)
= (1/6) * (2/6)
= 1/18
Scenario 2: The first dice shows a number less than or equal to 2 and the second dice shows two.
The probability of the first dice showing a number less than or equal to 2 is 2/6, as there are two favorable outcomes (getting a one or a two) out of six possible outcomes.
The probability of the second dice showing two is 1/6, as there is only one favorable outcome (getting a two) out of six possible outcomes.
Using the multiplication rule for independent events, the probability of both events occurring is:
P(First dice shows a number less than or equal to 2 and second dice shows two) = P(First dice shows a number less than or equal to 2) * P(Second dice shows two)
= (2/6) * (1/6)
= 1/18
Now, to find the probability that only one dice shows two, we need to add the probabilities of both scenarios:
P(Only one dice shows two) = P(First dice shows two and second dice shows a number less than or equal to 2) + P(First dice shows a number less than or equal to 2 and second dice shows two)
= 1/18 + 1/18
= 2/18
= 1/9
Therefore, the probability that only one dice shows two is 1/9, which is not listed as an option. None of the given options match the correct answer.
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Two fairdices are thrown. Giventh at the sum of the dice is less than or equal to 4, find the probability that only one dice shows two.a)1/4b)1/2c)2/3d)1/3Correct answer is option 'D'. Can you explain this answer?
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