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Probability, MET2 2008 VCAA 14 MC

The minimum number of times that a fair coin can be tossed so that the probability of obtaining a head on each trial is less than 0.0005 is

A.     `8`

B.     `9`

C.   `10`

D.   `11`

E.   `12`

Show Answers Only

`D`

Show Worked Solution

`text(Let)\ \ X = text(Number of heads,)`

`X ∼ text(Bi) (n, 1/2)`

`text(Pr) (X = n)` `< 0.0005`
`((n), (n)) (1/2)^n (1/2)^0` `< 0.0005`
`n` `> 10.97`

`:. n_min = 11`

`=>   D`

Filed Under: Binomial Tagged With: Band 4, smc-638-15-Find n given probability, smc-638-40-Inverse Binom N (CAS)

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