Two fair dice are thrown simultaneously. Find the probability that both the dice show different numbers.
• 1/6
• 5/6
• 32/36
• 29/36
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Answers
Option b
Step-by-step explanation:
Given :-
Two fair dice are thrown simultaneously.
To find :-
Find the probability that both the dice show different numbers. ?
Solution :-
Given that
Two dice are thrown simultaneously
We know that
n dice are thrown simultaneously then the number of possible outcomes are 6^n
We have ,n = 2
Number of all possible outcomes = 6² = 6×6 = 36
They are :
(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).
The different numbers on top face of both dice are :
(1,2),(1,3),(1,4),(1,5),(1,6),
(2,1),(2,3),(2,4),(2,5),(2,6),
(3,1),(3,2),(3,4),(3,5),(3,6),
(4,1),(4,2),(4,3),(4,5),(4,6),
(5,1),(5,2),(5,3),(5,4),(5,6),
(6,1),(6,2),(6,3),(6,4),(6,5).
Total number of favourable outcomes to different numbers = 30
We know that
The probability of an event E is P(E) = Number of favourable outcomes to E/Total number of all possible outcomes.
Probability of getting that both dice show different numbers = 30/36
=> (5×6)/(6×6)
=> 5/6
Answer:-
Probability of getting both numbers are different in the top face of the dice is 5/6
Used formulae:-
- n dice are thrown simultaneously then the number of possible outcomes are 6^n
- The probability of an event E is P(E) = Number of favourable outcomes to E/Total number of all possible outcomes.
Answer:
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Step-by-step explanation:
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