CRE 2 - Rolling Dice | Modern Math - Probability

Answer: Option B

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Explanation :

When a dice is rolled total possible outcomes (i.e., 1 or 2 or 3 or 4 or 5 or 6) = 6.
    
Desired outcome (i.e., 6) = 1.
    
∴ Required probability = 1/6.

Hence, option (b).

Answer: Option A

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Explanation :

When a dice is rolled total possible outcomes (i.e., 1 or 2 or 3 or 4 or 5 or 6) = 6.
    
Desired outcomes (i.e., 2 or 4 or 6) = 3.

∴ Required probability = 3/6 = 1/2.

Hence, option (a).

Answer: Option C

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Explanation :

When a dice is rolled total possible outcomes (i.e., 1 or 2 or 3 or 4 or 5 or 6) = 6.
    
Desired outcomes (i.e., 2 or 3 or 4 or 5 or 6) = 5.

∴ Required probability = 5/6.

Hence, option (c).

Answer: Option A

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Explanation :

When a dice is rolled total possible outcomes (i.e., 1 or 2 or 3 or 4 or 5 or 6) = 6.
    
Desired outcomes (i.e., 1 or 4 or 6) = 3.

∴ Required probability = 3/6 = 1/2.

Hence, option (a).

Answer: Option B

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Explanation :

When 2 die are rolled total possible outcomes = 6 × 6 = 36

Total outcomes: 

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For the sum to be 7, desired outcomes = {(1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3)} = 6.

∴ Required probability = 6/36 = 1/6.

Hence, option (b).

Answer: Option C

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Explanation :

When 2 die are rolled total possible outcomes = 6 × 6 = 36

Outcomes for sum to be 2: {(1, 1)} i.e., 1 outcome.
Outcomes for sum to be 12: {(6, 6)} i.e., 1 outcome.

Outcomes for sum to be 3: {(1, 2) or (2, 1)} i.e., 2 outcomes.
Outcomes for sum to be 11: {(6, 5) or (5, 6)} i.e., 2 outcomes.

Outcomes for sum to be 4: {(1, 3) or (3, 1) or (2, 2)} i.e., 3 outcomes.
Outcomes for sum to be 10: {(6, 4) or (4, 6) or (5, 5)} i.e., 3 outcomes.

Similarly, we can draw the following relation between sum and number of outcomes.

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For the sum to exceed 7, desired number of outcomes = 5 + 4 + 3 + 2 + 1 = 15.

∴ Required probability = 15/36 = 5/12.

Hence, option (c).

Answer: Option B

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Explanation :

When 2 die are rolled total possible outcomes = 6 × 6 = 36

Relation between sum and number of outcomes.

​​​​​​​

For the sum to not exceed 5, desired number of outcomes = 1 + 2 + 3 + 4 = 10.

∴ Required probability = 10/36 = 5/18.

Hence, option (b).

Answer: Option D

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Explanation :

When 2 die are rolled total possible outcomes = 6 × 6 = 36

There are 3 possibilities for each dice i.e., 2 or 4 or 6.

∴ Total desired outcomes = 3 × 3 = 9.

∴ Required probability = 9/36 = 1/4.

Hence, option (d).

Answer: Option C

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Explanation :

When 2 die are rolled total possible outcomes = 6 × 6 = 36

Relation between sum and number of outcomes.

​​​​​​​

∴ Total desired outcomes for sum to be prime = 1 + 2 + 4 + 6 + 2 = 15.

∴ Required probability = 15/36 = 5/12.

Hence, option (c).