Three dice are thrown simultaneously. Find the probability of getting a number on at least one die equal to even prime number.
- 1/7
- 91/216
- 31/36
- 5/6
Answer [Detailed Solution Below]
Option 2 : 91/216
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Child Development and Pedagogy Mock Test
10 Questions 10 Marks 10 Mins
Given:
Three dice are thrown simultaneously.
Concepts used:
A fair die is numbered from 1 to 6 with probability of coming of each number being 1/6.
Total number of outcomes on roll of three dice = 216
Calculation:
Even prime numbers out of 1 to 6 is 2.
⇒ Probability of getting number of outcomes in which even prime number appears on at least one die = P [Number of outcomes in which 2 appears on one die + Number of outcomes in which 2 appears on two dice + Number of outcomes in which 2 appears on three dice]
⇒ P [Number of outcomes in which even prime number appears on at least one die] = P {[3 × 1/6 × 5/6 × 5/6]} + P {[3 × 1/6 × 1/6 × 5/6]} + P {[1/6 × 1/6 × 1/6]} = 91/216
∴ Probability of getting a number on at least one die equal to even prime number is 91/216.
Alternative solution:
The only even prime number out of 6 numbers [1, 2, 3, 4, 5, 6] is 2.
⇒ P [2 comes on at least one die] = 1 - P [2 comes on neither die]
⇒ P [2 comes up on at least one die] = 1 - [5/6 × 5/6 × 5/6]
⇒ P [2 comes up on at least one die] = 91/216.
∴ Probability of getting a number on at least one die equal to even prime number is 91/216.
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I am having a hard time wrapping my head around this and am sure that my answers are wrong.
There are three dice.
A. Chance of getting exactly one six on the three dice. $$[1/6] * 3 = 1/3$$
B. Chance of getting exactly two sixes. $$[1/6 * 1/6] * 1.5 = 1/24$$
C. Chance of getting exactly $~3~$ sixes. $$1/6 * 1/6 * 1/6 = 1/216$$
D. Chance of any combination of A, B and C $$1/3 + 1/24 + 1/216= 72/216 + 9/216 + 1/216 = 82/216$$
nmasanta
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asked Oct 14, 2013 at 9:04
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A. There is a total of 6^3=216 combinations if you roll 3 dice. There are 5^2x3=75 combinations that you will get one 6. Thus there is a 75/216=25/72 chance of getting only one 6 when rolling 3 dice.
B. There are 5x3 combinations that you will get 2 6s. Thus there is a 15/216=5/72 chance of getting a 2 6s when rolling 3 dice.
C. There is 1 combination where you will get 3 6s. Thus there is a 1/216 chance you will get 3 6s when rolling 3 dice. [Good job you got this correct]
D. There is a 75+15+1/216=91/216 chance of any of them happening.
answered Oct 14, 2013 at 9:41
EpicGuyEpicGuy
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Hint for A: what is the chance that no sixes appear? If you know that chance then you automatically know the chance that sixes do appear.
answered Oct 14, 2013 at 9:13
drhabdrhab
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The chance of getting at least one 6 with three dice is 91/216 because if you subtract 125/216 [the probability of rolling three dice without getting a 6] from 216/216 [the probability of any combination of numbers], you get 91/216.
answered Nov 26, 2013 at 16:09
user111236user111236
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