If you roll one fair six-sided die, what is the probability that the

Question

If you roll one fair six-sided die, what is the probability that the number is even or less than 4?

(A) 1/6
(B) 1/3
(C) 2/ 3
(D) 3/4
(E) 5/6

jarnugirdhar · Answer

P(E U < 4) = P(E) + P(<4) - P(E & < 4)

= 3/6 + 3/6 - 1/6
= 5/6

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kungfury42 · Answer

Total possible outcomes = 6 {1, 2, 3, 4, 5, and 6}
Favorable outcomes = 5 {1, 2, 3, 4, and 6}

Probability = 5/6

Hence, option E.

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emont · Answer

hi i thought or means you have to add the probabilty of each?

Bunuel · Answer

The probability of getting a number less than 4 is 1/2 (1,  2 , or 3), and the probability of getting an even number is also 1/2 ( 2 , 4, or 6). However, both of these probabilities include the number 2, which is both even and less than 4, so its probability (1/6) gets counted twice. To avoid double counting, we subtract the probability of rolling a 2:

1/2 + 1/2 - 1/6 = 5/6.

You should have noticed that adding 1/2 + 1/2 gives 1, which implies a 100% probability, and that's clearly not correct for this event.

Alternatively, you could recognize that the only outcome that isn’t favorable is 5, which has a probability of 1/6. Therefore, the probability of the favorable outcomes is 1 - 1/6 = 5/6.

Or, you could list the favorable outcomes: 1, 2, 3 (numbers less than 4), and 4, 6 (even numbers). This gives a total probability of 5/6.

BrushMyQuant · Answer

If you roll one fair six-sided die, what is the probability that the number is even or less than 4?

Number will be even or less than 4 in all cases except when the roll is 5 i.e. only 1 case (1,2,3 are less than 4 and 4 and 6 are even)
=> Number is even or less than 4 in 5 cases

=> P(Number is even or less than 4) =  \frac{5}{6}

So,  Answer will be E 
Hope it helps!

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