Two dice are rolled probability of getting a total of 6 given that both faces are similar is
Answers
Answer:
Assuming that the dice are unbiased or not " loaded".
Each side has the same probability, is 1/6 =0.16667, to turn up when rolled, if the die (D) is unbiased. The probability of a side turning up on D1 when 2 dice ( D1,D2) are rolled, is independent of the side turning up in D2. So this is an independent event.
How many ways can one get a sum total of 6 if D1 &D2 are rolled at the same time?
These are the possibilities
Case 1.
D1 =1 & D2=5
Or
D1= 5 & D2=1
Case 2.
D1 =2 & D2=4
Or
D1= 4 & D2= 2
Case 3. D1=3, D2=3
P3 =0.027778
Let's say, P 1 the probability for case 1 and P2 for case 2. There are no other cases.
The final probability P and is the sum total P = P1 + P2 + P3 the probability law of mutually exclusive events.
P1= 0.02778+ 0.02778 =0.055558
P2= 0.02778+0.02778 =0.055558
Same way,
P3=0.027778, when there is only one way to get the sum 6.
So, P = 0.138894
Step-by-step explanation:
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What is the probability of getting a sum of 6 if two dice are thrown?
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35 Questions and Answers
Sumedha Sengupta, Former Member : ASA, ASQC, Sigma XI
Answered 5 years ago · Author has 792 answers and 927.5K answer views
What is the probability of getting a sum of 6 if two dice are thrown?
Two dice
Assuming that the dice are unbiased or not " loaded".
Each side has the same probability, is 1/6 =0.16667, to turn up when rolled, if the die (D) is unbiased. The probability of a side turning up on D1 when 2 dice ( D1,D2) are rolled, is independent of the side turning up in D2. So this is an independent event.
How many ways can one get a sum total of 6 if D1 &D2 are rolled at the same time?
These are the possibilities
Case 1.
D1 =1 & D2=5
Or
D1= 5 & D2=1
Case 2.
D1 =2 & D2=4
Or
D1= 4 & D2= 2
Case 3. D1=3, D2=3
P3 =0.027778
Let's say, P 1 the probability for case 1 and P2 for case 2. There are no other cases.
The final probability P and is the sum total P = P1 + P2 + P3 the probability law of mutually exclusive events.
P1= 0.02778+ 0.02778 =0.055558
P2= 0.02778+0.02778 =0.055558
Same way,
P3=0.027778, when there is only one way to get the sum 6.
So, P = 0.138894
Based on truncating at the sixth decimal place.
A visual representation with two unbiased dice and the possible cases would also give the same result and is a short cut method. I like to derive from the basics.
42K viewsView 6 Upvoters
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Other Answers
John Abraham
Answered 1 year ago
What is the probability of getting a sum of 6 if two dice are thrown?
The answer would be 5/36 because the number of possible outcomes is 36, and the possible ways to get a sum of six are (1, 5), (2, 4), (3, 3), (4, 2), (5, 1). There are 5 ways and 36 possible outcomes in total, so 5/36 is the answer. There is one more solution as well (technically). The order could matter in this problem, so (3, 3) and (3, 3) can be perceived to be different. With this method of solving the problem, there would be 42 different outcomes and 6 ways to obtain a sum of six, making the answer 1/7. The reason (3, 3) and (3, 3) are different is because it would look like this with A being the first dice and B being the 2nd: (1A, 5B), (2A, 4B), (3A, 3B), (3B, 3A), (4A, 2B), and (5A, 1B). These two solutions can be both counted as correct based on the way that one perceives it. The second solution is obtained using permutations instead of simple combinations. The first solution (5/36) is widely regarded as the correct answer (which is mostly true), but technically 1/7 is also correct.