If a 6-sided fair die with sides 1, 2, 3, 4, 5, and 6 is rolled twice,

Question

If a 6-sided fair die with sides 1, 2, 3, 4, 5, and 6 is rolled twice, what is the probability that it will land on an even number both times? (answer is fraction)

shwetakoshija · Answer

Given: 
 
 A fair 6-sided die with faces {1, 2, 3, 4, 5, 6}. 
 The die is rolled  twice .

To find:  Probability that  both rolls  land on even numbers.

Solution: 
Let's calculate the probability of getting an even number on  one roll 
 
 Even numbers on the die: {2, 4, 6} → 3 outcomes. 
 Since there are 3 favorable outcomes out of 6 total, the probability of an even number on any roll =  3/6 = 1/2

Since the two rolls are independent, probability of even number on  both rolls  = (1/2) × (1/2) = 1/4 -----

Correct Answer:  1/4

Shweta Koshija  
 GMAT, GRE, SAT Coach for 10+ years

Sajjad1994 · Answer

OE

This is an  “and”  problem with two independent events. For each roll of the die, the probability of an even number is 3/6, which simplifies to 1/2. Multiply the individual probabilities because the two outcomes are independent:  \frac{1}{2}*\frac{1}{2}=\frac{1}{4}

Answer: 1/4

If a 6-sided fair die with sides 1, 2, 3, 4, 5, and 6 is rolled twice,

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