If the two dice are thrown together, then the probability of getting the same number on both dice is
A)1/2
B)1/12
C)1/3
D)1/6
I need step by step explanation not option
Answers
Answer:
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Step-by-step explanation:
Probability of an event = Number of outcomes favourable to that event/ Number of all possible outcomes.
The set of all possible outcomes is called the sample space and is denoted by S.
When two dice are tossed, the possible outcomes 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). Hence n(S) = 36.
But we want the desired event E that the number should be same on both dice. Such outcomes (1,1),(2,2),(3,3)(4,4),(5,5) and (6,6). We have 6 desired outcomes. So n(E) = 6
Hence the probability of getting same number. on both dice = n(E)/ n(S) = 6/36 = 1/6
Answer:
Total no. Of outcomes when 2 dice are thrown= 6× 6= 36
Favourable outcomes (1,1), (2,2), (3,3), (4,4,) (5,5) and (6,6).
No. Of favourable outcomes= 6
Probability ( same no. On both dice) = no.of favourable outcomes/ total no.of outcomes
Probability ( same no. On both dice) = no.of favourable outcomes/ total no.of outcomes
Probability ( same no. On both dice) = 6 / 36
= 1 / 6
option D
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