1. An urn contains seven red ballsand three white balls. A sample of2 balls is s

Question

1. An urn contains seven red ballsand three white balls. A sample of2 balls is selected at random from theurn. What is the probability that at least one of the balls isred?
2. A factory produces fuses, which are packaged in boxes of10. Threefuses are selected at random from each box for inspection. The boxis rejected if at least one of these three fuses is defective. What is the probabilitythat a box containing three defectivefuses will be rejected?
Please include steps! 1. An urn contains seven red ballsand three white balls. A sample of2 balls is selected at random from theurn. What is the probability that at least one of the balls isred?
2. A factory produces fuses, which are packaged in boxes of10. Threefuses are selected at random from each box for inspection. The boxis rejected if at least one of these three fuses is defective. What is the probabilitythat a box containing three defectivefuses will be rejected?
Please include steps!

Explanation / Answer

CRAMSTER POLICY IS ONEQUESTION PER POST
ANSWERING I Q.
PLEASE POST II Q SEPARATELY
Question Details: 1. An urn contains seven red ballsand three white balls. A sample of2 balls is selected at random
from the urn. What is the probability that at least one ofthe balls is red?
I AM SORRY I MISREAD THE QUESTION AS DRAWING ONEWHITE AND ONE RED BALL . CORRECTING THE SOLUTION AS DESIRED FOR"probability that at least one of the balls is red?"
ONCE AGAIN SORRY FOR INCONVENIENCE.

THERE ARE IN ALL 7+3=10 BALLS INCLUDING 3 WHITE BALLS
LET US FIND PROBABILITY OF DRAWING BOTH WHITE BALLS AND THENSUBTRACT
IT FROM TOTAL PROBABILITY OF 1 TO GET THE REQUIREDANSWER.

I BALL DRAWN IS WHITE ....P=3/10
NOW THERE ARE 9 BALLS INCLUDING 2 WHITE BALLS .
SO II BALL ALSO BEING WHITE ....P= 2/9

P=[3/10][2/9]=1/15
HENCE REQUIRED PROBABILITY ..THAT IS ["probability that at least one of the balls is red?"]
= 1- 1/15 = 14/15

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