The rolls of the dice are independent, i.e. the outcome of the second die doesn't depend in any way on the outcome of the first die.
In cases like this, the probability of two events happening one after the other is the multiplication of the probabilities of the two events.
So, the probability of rolling two 6s is the multiplication of the probabilities of rolling a six with the first die, and another six with the second:

Similarly,

Actually, you can see that the probability of rolling any ordered couple is always 1/36, since the probability of rolling any number on both dice is 1/6:

Yeah but what is the question?
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Answer:
After 5 months the cost of the two phones and monthly service be the same.
Step-by-step explanation:
1st service cost = $50 + $40x, where "x" represents the number of months
2nd service cost = $50x
Now we have to find the number of months the cost of the two phones and monthly service be the same.
Now we have to equivate and find the value of x.
50x = 50 + 40x
Subtracting 40x from both sides, we get
50x - 40x = 50 + 40x - 40x
10x = 50
Dividing both sides by 10, we get
x = 50/10
x = 5
After 5 months the cost of the two phones and monthly service be the same.
Hope you will understand the concept.
Thank you.
Answer:
8(5) + 8(25) + 8(125) + 8(625) +8(3125)= 10(3125 - 1)=31240
Hence proved Conjecture is correct
L.H.S=R.H.S
Step-by-step explanation:
Consider the pattern:
8(5)=10(5-1)=40
8(5) + 8(25) = 10(25 - 1) =240
8(5) + 8(25) + 8(125) = 10(125 - 1) =1240
8(5) + 8(25) + 8(125) + 8(625) = 10(625 - 1)=6240
According to inductive reasoning next term of pattern will become:
8(5) + 8(25) + 8(125) + 8(625) +8(3125)= 10(3125 - 1)=31240
Checking whether conjecture is correct or not:
Consider L.H.S:
8(5) + 8(25) + 8(125) + 8(625) +8(3125)
40+200+1000+5000+25000
31240
R.H.S:
31240
Hence proved Conjecture is correct
L.H.S=R.H.S