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There are two identical dice with a single letter on each of the faces . The following six letters : Q, R, S, T, U and V, one on each of the faces. Any of the six outcomes are equally likely.
The two dice are thrown once independently at random.
What is the probability that the outcomes on the dice were composed only of any combination of the following possible outcomes : Q, U and V?
The two dice are thrown once independently at random.
What is the probability that the outcomes on the dice were composed only of any combination of the following possible outcomes : Q, U and V?
- a)1/4
- b)3/4
- c)1/6
- d)5/36
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
There are two identical dice with a single letter on each of the faces...
Given two dice.
P(E) = Favourable/Total
P(E) = Favourable/Total
P(E) = 3/6 x 3/6 = 1/4
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There are two identical dice with a single letter on each of the faces...
To solve this problem, we need to determine the total number of possible outcomes and the number of outcomes that meet the given condition.
Total Number of Outcomes:
Since there are two identical dice and each dice has 6 possible outcomes (Q, R, S, T, U, V), the total number of possible outcomes is 6 * 6 = 36.
Outcomes that meet the condition:
We need to find the outcomes that are composed only of the letters Q, U, and V.
There are three possible outcomes that meet this condition:
1. Q on the first dice and U on the second dice.
2. Q on the first dice and V on the second dice.
3. U on the first dice and V on the second dice.
So, the number of outcomes that meet the condition is 3.
Probability Calculation:
The probability is calculated by dividing the number of outcomes that meet the condition by the total number of possible outcomes.
Probability = Number of outcomes that meet the condition / Total number of possible outcomes
Probability = 3 / 36 = 1 / 12
However, the question asks for the probability that the outcomes were composed only of any combination of the letters Q, U, and V. This means that we need to consider the three possible outcomes individually as well as when they occur in combination.
1. Q on the first dice and U on the second dice:
The probability of this outcome is 1/36.
2. Q on the first dice and V on the second dice:
The probability of this outcome is also 1/36.
3. U on the first dice and V on the second dice:
The probability of this outcome is also 1/36.
Since these three outcomes are mutually exclusive (they cannot occur at the same time), we can add their probabilities to find the probability that any one of these outcomes occurs.
Probability = 1/36 + 1/36 + 1/36 = 3/36 = 1/12
Therefore, the probability that the outcomes on the dice were composed only of any combination of Q, U, and V is 1/12.
However, the options provided in the question are not in the form of fractions. To convert 1/12 to a fraction with a denominator of 36, we multiply the numerator and denominator by 3.
Probability = (1/12) * (3/3) = 3/36 = 1/12 = 1/4
So, the correct answer is option A: 1/4.
Total Number of Outcomes:
Since there are two identical dice and each dice has 6 possible outcomes (Q, R, S, T, U, V), the total number of possible outcomes is 6 * 6 = 36.
Outcomes that meet the condition:
We need to find the outcomes that are composed only of the letters Q, U, and V.
There are three possible outcomes that meet this condition:
1. Q on the first dice and U on the second dice.
2. Q on the first dice and V on the second dice.
3. U on the first dice and V on the second dice.
So, the number of outcomes that meet the condition is 3.
Probability Calculation:
The probability is calculated by dividing the number of outcomes that meet the condition by the total number of possible outcomes.
Probability = Number of outcomes that meet the condition / Total number of possible outcomes
Probability = 3 / 36 = 1 / 12
However, the question asks for the probability that the outcomes were composed only of any combination of the letters Q, U, and V. This means that we need to consider the three possible outcomes individually as well as when they occur in combination.
1. Q on the first dice and U on the second dice:
The probability of this outcome is 1/36.
2. Q on the first dice and V on the second dice:
The probability of this outcome is also 1/36.
3. U on the first dice and V on the second dice:
The probability of this outcome is also 1/36.
Since these three outcomes are mutually exclusive (they cannot occur at the same time), we can add their probabilities to find the probability that any one of these outcomes occurs.
Probability = 1/36 + 1/36 + 1/36 = 3/36 = 1/12
Therefore, the probability that the outcomes on the dice were composed only of any combination of Q, U, and V is 1/12.
However, the options provided in the question are not in the form of fractions. To convert 1/12 to a fraction with a denominator of 36, we multiply the numerator and denominator by 3.
Probability = (1/12) * (3/3) = 3/36 = 1/12 = 1/4
So, the correct answer is option A: 1/4.
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