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Two dice are thrown together. Find the probability of getting a multiple of 2 on one dice and multiple of 3 on the other.
- a)2/3
- b)5/18
- c)1/13
- d)None of the above.
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two dice are thrown together. Find the probability of getting a multip...
Two dice are thrown simultaneously
S={(1,1),(1,2),(1,3),(1,4),(1,5), (1,6)
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}
n(s)=36
Event A : getting multiple of 2 on one die and multiple of 3 on other die
A={(2,3)(2,6)(4,3)(4,6) (6,3)(6,6)(6,2)(6,4)(3,2)(3,6)}
n(A)=10
p(A)=n(A)/n(s)
=10/36
=5/18
S={(1,1),(1,2),(1,3),(1,4),(1,5), (1,6)
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}
n(s)=36
Event A : getting multiple of 2 on one die and multiple of 3 on other die
A={(2,3)(2,6)(4,3)(4,6) (6,3)(6,6)(6,2)(6,4)(3,2)(3,6)}
n(A)=10
p(A)=n(A)/n(s)
=10/36
=5/18
Most Upvoted Answer
Two dice are thrown together. Find the probability of getting a multip...
Solution:
When two dice are thrown together, the number of possible outcomes is 6 x 6 = 36.
Let's list down the possible outcomes of getting a multiple of 2 on one dice and multiple of 3 on the other.
- The multiples of 2 on one dice are 2, 4, and 6.
- The multiples of 3 on the other dice are 3 and 6.
So, the possible outcomes are:
- (2,3), (2,6), (4,3), (4,6), (6,3), and (6,6).
Out of the 36 possible outcomes, there are 6 outcomes that satisfy the condition.
Therefore, the probability of getting a multiple of 2 on one dice and multiple of 3 on the other is:
6/36 = 1/6
Simplifying, we get:
1/6 = (1/2) x (1/3)
Therefore, the probability of getting a multiple of 2 on one dice and multiple of 3 on the other is the product of the probabilities of getting a multiple of 2 and 3 on the two dice, respectively.
Hence, the correct answer is option 'B' (5/18).
When two dice are thrown together, the number of possible outcomes is 6 x 6 = 36.
Let's list down the possible outcomes of getting a multiple of 2 on one dice and multiple of 3 on the other.
- The multiples of 2 on one dice are 2, 4, and 6.
- The multiples of 3 on the other dice are 3 and 6.
So, the possible outcomes are:
- (2,3), (2,6), (4,3), (4,6), (6,3), and (6,6).
Out of the 36 possible outcomes, there are 6 outcomes that satisfy the condition.
Therefore, the probability of getting a multiple of 2 on one dice and multiple of 3 on the other is:
6/36 = 1/6
Simplifying, we get:
1/6 = (1/2) x (1/3)
Therefore, the probability of getting a multiple of 2 on one dice and multiple of 3 on the other is the product of the probabilities of getting a multiple of 2 and 3 on the two dice, respectively.
Hence, the correct answer is option 'B' (5/18).
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