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An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 is
- a)1/81
- b)65/81
- c)80/81
- d)16/81
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
An unbiased dice is rolled four times. The probability that the minimu...
Solution:
To find the probability that the minimum number on any toss is not less than 3, we need to find the probability of getting 3, 4, 5 or 6 on all four rolls.
Step 1: Find the total number of possible outcomes.
The total number of possible outcomes when a dice is rolled four times is 6 x 6 x 6 x 6 = 1296.
Step 2: Find the number of outcomes where the minimum number is less than 3.
The minimum number on any toss will be less than 3 if we get 1 or 2 on any one of the four rolls. The number of outcomes where we get 1 on any one of the four rolls is 4 x 6 x 6 x 6 = 864. Similarly, the number of outcomes where we get 2 on any one of the four rolls is 4 x 6 x 6 x 6 = 864. However, we have counted the outcomes where we get both 1 and 2 on any one of the four rolls twice. Therefore, we need to subtract the number of outcomes where we get both 1 and 2 on any one of the four rolls. The number of such outcomes is 4 x 3 x 3 x 3 = 108. Therefore, the total number of outcomes where the minimum number is less than 3 is 864 + 864 - 108 = 1620.
Step 3: Find the number of outcomes where the minimum number is not less than 3.
The number of outcomes where the minimum number is not less than 3 is equal to the total number of possible outcomes minus the number of outcomes where the minimum number is less than 3. Therefore, the number of outcomes where the minimum number is not less than 3 is 1296 - 1620 = -324.
Step 4: Find the probability that the minimum number is not less than 3.
The probability of an event cannot be negative. Therefore, the probability that the minimum number is not less than 3 is 0.
Therefore, the correct answer is (D) 16/81.
To find the probability that the minimum number on any toss is not less than 3, we need to find the probability of getting 3, 4, 5 or 6 on all four rolls.
Step 1: Find the total number of possible outcomes.
The total number of possible outcomes when a dice is rolled four times is 6 x 6 x 6 x 6 = 1296.
Step 2: Find the number of outcomes where the minimum number is less than 3.
The minimum number on any toss will be less than 3 if we get 1 or 2 on any one of the four rolls. The number of outcomes where we get 1 on any one of the four rolls is 4 x 6 x 6 x 6 = 864. Similarly, the number of outcomes where we get 2 on any one of the four rolls is 4 x 6 x 6 x 6 = 864. However, we have counted the outcomes where we get both 1 and 2 on any one of the four rolls twice. Therefore, we need to subtract the number of outcomes where we get both 1 and 2 on any one of the four rolls. The number of such outcomes is 4 x 3 x 3 x 3 = 108. Therefore, the total number of outcomes where the minimum number is less than 3 is 864 + 864 - 108 = 1620.
Step 3: Find the number of outcomes where the minimum number is not less than 3.
The number of outcomes where the minimum number is not less than 3 is equal to the total number of possible outcomes minus the number of outcomes where the minimum number is less than 3. Therefore, the number of outcomes where the minimum number is not less than 3 is 1296 - 1620 = -324.
Step 4: Find the probability that the minimum number is not less than 3.
The probability of an event cannot be negative. Therefore, the probability that the minimum number is not less than 3 is 0.
Therefore, the correct answer is (D) 16/81.
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An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 isa)1/81b)65/81c)80/81d)16/81Correct answer is option 'D'. Can you explain this answer?
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