Anurn contains 6 red,4 blue ,2 green and 3yellow marbles
If four marbles are picked at random , what is the probability that at least one is blue ?

Options

A. `(4)/(15)`
B. `(69)/(91)`
C. `(11)/(15)`
D. `(22)/(91)`

Answer

B

Explanation

Number of way of selecting 4 marbles out of 15 marbles
`=""^(15)C_(4)=(15xx14xx13xx12)/(4xx3xx2xx1)=1365`
Number of ways of selecting 4 marbles when no one is blue `=""^(11)C_(4)=(11xx10xx9xx8)/(4xx3xx2xx1)=330`
Probability of getting 4 marbles (when no one is blue ) `=(330)/(1365)=(22)/(91)`
Probability that at least one is blue `=1-(22)/(91)=(69)/(91)`