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Sirisha

· started a discussion

· 1 Months ago

probability (Question:1056391.0)

Any other clear explanation for the doubt

Question:
A die is rolled three times. The probability of getting a larger number than the previous number each time is:
Options:
A) 7/54 
B) 5/54
C) 11/54 
D) 6/54
E) None of these
Solution:

The total no. of ways = 6 × 6 × 6 = 216

Now we can fix the middle number as 2, 3, 4, 5.

∴ the no. of favorable ways:

if 2nd digit is 2 =1 × 1× 4 = 4

if 2nd digit is 3 = 2 × 1 × 3 = 6

if 2nd digit is 4 = 3 × 1   × 2 = 6

if 2nd digit is 5 = 4 × 1 × 1  = 4 i.e.,4 + 6 + 6 + 4 = 20

∴ Required probability is = 20/216 = 5/54.


Alternative method

Total no. of possible outcome = 63 = 216

Favorable outcome = \(^6C_3\)x 1 = 20 

Probability = \(\frac{20}{216}\) 

                = 5 /54.

Knowledge Expert

· commented

· 1 Months ago

Dear student,
We have updated answer solution. kindly re-check.

Regards
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