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Two fair dice are thrown. Find the probability of getting
(i) sum of numbers divisible by 2 or 4.
- a)1/2
- b)3/4
- c)1/3
- d)2/3
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Two fair dice are thrown. Find the probability of getting(i) sum of nu...
Positive outcomes are 2(1 way), 4(3 ways), 6(5 ways) 8(5 ways), 10 (3 ways), 12 (lway). Thus, 18/36= 1/2
This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
Two fair dice are thrown. Find the probability of getting(i) sum of nu...
Solution:
Possible outcomes of throwing two dice:
Let A= event of getting a sum of numbers divisible by 2 or 4.
Let B= event of getting a sum of numbers not divisible by 2 or 4.
Now, A and B are mutually exclusive events. i.e.
A ∩ B = ϕ
Probability of getting a sum of numbers divisible by 2 or 4:
Let's list down the possible outcomes of throwing two dice and getting a sum of numbers divisible by 2 or 4:
1+1=2
1+3=4
1+5=6
2+2=4
2+4=6
2+6=8
3+1=4
3+3=6
3+5=8
4+2=6
4+4=8
4+6=10
5+1=6
5+3=8
5+5=10
6+2=8
6+4=10
6+6=12
There are 16 possible outcomes of throwing two dice.
Out of these 16 possible outcomes, 8 outcomes satisfy the condition of getting a sum of numbers divisible by 2 or 4.
Therefore, the probability of getting a sum of numbers divisible by 2 or 4 is:
P(A) = Number of outcomes satisfying the condition of A / Total number of possible outcomes of throwing two dice
P(A) = 8/16
P(A) = 1/2
Hence, the correct option is (a) 1/2.
Possible outcomes of throwing two dice:
Let A= event of getting a sum of numbers divisible by 2 or 4.
Let B= event of getting a sum of numbers not divisible by 2 or 4.
Now, A and B are mutually exclusive events. i.e.
A ∩ B = ϕ
Probability of getting a sum of numbers divisible by 2 or 4:
Let's list down the possible outcomes of throwing two dice and getting a sum of numbers divisible by 2 or 4:
1+1=2
1+3=4
1+5=6
2+2=4
2+4=6
2+6=8
3+1=4
3+3=6
3+5=8
4+2=6
4+4=8
4+6=10
5+1=6
5+3=8
5+5=10
6+2=8
6+4=10
6+6=12
There are 16 possible outcomes of throwing two dice.
Out of these 16 possible outcomes, 8 outcomes satisfy the condition of getting a sum of numbers divisible by 2 or 4.
Therefore, the probability of getting a sum of numbers divisible by 2 or 4 is:
P(A) = Number of outcomes satisfying the condition of A / Total number of possible outcomes of throwing two dice
P(A) = 8/16
P(A) = 1/2
Hence, the correct option is (a) 1/2.
Community Answer
Two fair dice are thrown. Find the probability of getting(i) sum of nu...
Both are same xy/100.
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