"Two different dice are thrown together. Find the probability of:
(i) getting a number greater than 3 on each die
(ii) getting a total of 6 or 7 of the numbers on two dice"
Please tell what does the first point mean
Answers
Answer:
1/4, 11/36
Step-by-step explanation:
Total number of dice thrown = 2.
Possible outcomes n(S) = 6² = 36.
(i) each
Let E₁ be the event of getting a number greater than 3.
E₁ = [(4,4),(4,5),(4,6),(5,4),(5,5),(5,6),(6,4),(6,5),(6,6)]
n(E₁) = 9.
Required probability P(E) = n(E₁)/n(S)
= 9/36
= 1/4
(ii) Getting a total of 6 (or) 7:
Let E₂ be the event of getting a total of 6 (or) 7.
P(getting 6) = (3,3), (4,2), (2,4), (5,1), (1,5).
P(getting 7) = (6,1), (1,6), (2,5),(5,2), (3,4), (4,3)
P(6 ∪ 7) = 11/36.
Hope it helps!
Two different die are thrown together . So the number of possibilities will be 6 × 6 = 36 because in each case there are 6 chances and there are 6 cases . We can show that the number of possibilities is 36 by drawing the sample space :
Sample space
{ (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)}
So number of possibilities = 36 .
(i)
Getting a number greater than 3
There are only 3 numbers in a dice greater than 3 .
They are 4,5 and 6 . So we must get either 4,5 or 6 and it has to be from the possibilities .
Sample space
(4,4),(4,5),(4,6),
(5,4),(5,5),(5,6),
(6,4),(6,5),(6,6)
Hence there are 9 outcomes that are favourable .
Probability = number of favourable outcomes / number of possible outcomes
⇒ Probability = 9/36
⇒ Probability = 1/4
(ii)
Getting total 6 or 7
Sample space
(3,3),(2,4),(4,2),(1,5), (5,1) ,
(1,6),(6,1),(2,5),(5,2),(3,4),(4,3)
Hence the number of possibilities favourable is 5 + 6 = 11
Probability = number of favourable outcomes / number of possible outcomes