Five defective bolts are accidently mixed with twenty good ones. If four bolts are drawn at random from this lot, find the probability distribution of the number of defective bolts.

Explanation

loda Here, X represents the number of defective bolts drawn.

So, {X} can take values 0,1,2 or 3

because there are total 25 bolts ( 20 good +5 defectives) bolts.

`{n}({S})`= total possible ways of selecting 5 bolts` ={ }^{5} {C}_{4}`

P(X=0)=P( selecting no defective bolt )`=frac{{ }^{20} {C}_{4}}{{ }^{25} {C}_{4}}=frac{20 times 19 times 18 times 17}{25 times 24 times 23 times 22}=frac{969}{2530}`

P(X=1)=P( selecting 1 defective bolt and 3 good bolts )

`=frac{{ }^{5} {C}_{1} times{ }^{20} {C}_{3}}{{ }^{25} {C}_{4}}`

`=frac{frac{5 !}{4 !} times frac{20 !}{17 ! 3 !}}{frac{25 !}{21 ! 4 !}}`

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