A die is thrown 6 times. If "getting an odd number" is a success, what is the probability of (i) 5 successes? (ii) at least 5 successes? (iii) at most 5 successes?

Answer

N/a

Explanation

Probability of getting an even number in one throw of a die
`p=3/6=1/3`
`impliesq=1-1/2=1/2`
`n=6`
(i) `P(X=5)=.^(6)C_(5).p^(5).q^(6-5)`
`=6xx(1/2)^(5)(1/2)=3/32`
(ii) `P(Xge5)=P(X=5)+P(X=6)`
`=.^(6)C_(5).p^(5).q^(1)+.^(6)C_(6).p^(6).q^(0)`
`=6xx(1/2)^(5)(1/2)+1xx(1/2)^(6)`
`=7/64`
(iii) `P(Xle5)=1-P(X=6)`
`=1-.^(6)C_(6).p^(6).q^(0)`
`=1-(1/2)^(6)=63/64`