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Anurn contains 6 red,4 blue ,2 green and...

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 ?

A

`(4)/(15)`

B

`(69)/(91)`

C

`(11)/(15)`

D

`(22)/(91)`

Text Solution

Verified by Experts

The correct Answer is:
B
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)`
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Knowledge Check

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

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