A pair of dice is thrown 7 times. If getting a total of 7 is considered a success, what is the probability of (i) no success? (ii) 6 success? (iii) at least 6 success? (iv) at most 6 successes?

Options

A. `((5)/(6))^(7)`
B. `((1)/(6))^(7)`
C. `(1-(1)/(6^(7)))`
D. none of these

Answer

A

Explanation

In a single throw of a pair of dice , we have
`n(S ) =(6xx 6) =36`
Let E ={(1,6),(6,1),(2,5),(5,2),(3,4),(4,3)}
`:. , p =(6)/(36)= (1)/(6), q= (1-(1)/(6)) =(5)/(6)` and n=7
P (7 successes )`=.^(7)C_(7).((1)/(6))^(7) =((1)/(6))^(7)`
P(at most 6 successes ) =1 -P(7 successes ) `= 1- ((1)/(6))^(7) =(1-(1)/(6^(7)))`