Answer to Question #336392 in Statistics and Probability for Jenny

Question #336392

Suppose that 9 good fuses and 4 defective ones have been mixed up. To find the defective fuses, we test them one-by-one, at random. What is the probability that we are lucky and find both of the defective fuses in the first two tests?


1). With replacement


2). Without replacement


1
Expert's answer
2022-05-06T05:44:14-0400

1)


P(both defective)=49+4(49+4)=16169P(both\ defective)=\dfrac{4}{9+4}(\dfrac{4}{9+4})=\dfrac{16}{169}

2)


P(both defective)=49+4(419+41)=113P(both\ defective)=\dfrac{4}{9+4}(\dfrac{4-1}{9+4-1})=\dfrac{1}{13}


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