A fair six-sided die is rolled 4 times. What is the probabil

Question

A fair six-sided die is rolled 4 times. What is the probability that at least one result is repeated?

(A)  \frac{4}{9} 
(B)  \frac{5}{9} 
(C)  \frac{13}{18} 
(D)  \frac{31}{36} 
(E)  \frac{17}{18}

adconsectetur · Answer

AT LEAST ONE : HINT for the NOT method.

1- None repeated = 1- 6/6 * 5/6 * 4/6 * 3/6 = 13/18

Edskore · Answer

Classic "at least one" setup — the best move here is complementary counting.

1. Concept: P(at least one result is repeated) = 1 - P(no result is repeated at all).

2. P(no repeats): Roll 1 can be anything, so 6/6. Roll 2 must avoid roll 1, so 5/6. Roll 3 must avoid rolls 1 and 2, so 4/6. Roll 4 must avoid all three previous results, so 3/6.

3. P(no repeats) = (6/6)(5/6)(4/6)(3/6) = 360/1296 = 5/18.

4. P(at least one repeat) = 1 - 5/18 = 13/18.

The answer is (C).

The trap here is going direct — trying to count cases where exactly one result repeats, exactly two repeat, etc. That gets messy fast with overlapping scenarios. Whenever you see "at least one" in a probability Problem Solving question, flip it to the complement first and check if the "none" case is simpler to count. On this one, the no-repeats case is a clean sequential product, and the direct approach would take twice as long.

vasu1104 · Answer

die is rolled 4 times here.
find p( at least one result repeated)

now finding that would be too hell of work since any num can be repeated. so its better to find opposite of it.

means, p ( none will be repeated)=

for first we have 6 option available from all 6. 6/6 =1
then for second we have 5 option from all 6. 5/6
fir third we have 4 from all 6. 4/6
for last we have 3 from all 6. 3/6

so total = (6/6) (5/6) (4/6) (3/6)= 5/18

but we need to subtract this from 1 to find opposite of it.

1-5/18
13/18

option C

A fair six-sided die is rolled 4 times. What is the probabil

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GMAT Problem Solving (PS) Questions

A fair six-sided die is rolled 4 times. What is the probabil

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