Question #340126

There are 9 eggs out of which 4 are bad. 3 eggs are chosen at random.

1) In how many ways can we choose the 3 eggs from among the 9 eggs?

2) In how many ways can we choose 3 good eggs?

3) What is the probability that all selected eggs are good?

4) In how many ways can we choose 3 bad eggs?

5) What is the probability that all 3 selected eggs are bad ones?

6) What is the number of pairs of good eggs?

7) In how many ways can we choose 3 eggs out of which 1 is bad?

8) What is the probability that exactly one egg is bad?

9) What is the probability that at least one egg is bad?



1
Expert's answer
2022-05-17T22:59:35-0400

1)


(93)=84\dbinom{9}{3}=84

2)


(40)(943)=1(10)=10\dbinom{4}{0}\dbinom{9-4}{3}=1(10)=10

3)


P(3 good)=1084=542P(3\ good)=\dfrac{10}{84}=\dfrac{5}{42}

4)


(43)(940)=4(1)=4\dbinom{4}{3}\dbinom{9-4}{0}=4(1)=4



5)


P(3 bad)=484=121P(3\ bad)=\dfrac{4}{84}=\dfrac{1}{21}

6)


(942)=10\dbinom{9-4}{2}=10

7)


(41)(942)=4(10)=40\dbinom{4}{1}\dbinom{9-4}{2}=4(10)=40



8)


P(2 good & 1 bad)=4084=1021P(2\ good \ \&\ 1\ bad)=\dfrac{40}{84}=\dfrac{10}{21}

9)


P(at least 1 bad)=1542=3742P(at\ least\ 1\ bad)=1-\dfrac{5}{42}=\dfrac{37}{42}


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