Question

A lot of 20 bulbs contain 4 defective ones. one bulb is drawn at a random from the lot. What is the probability that this bulb us defective?
1) Suppose the bulb drawn is defective and is not replaced. Now,one bulb is drawn at a random from the rest. What is the probability that this bulb is not defective?

Answer 1

Answer:

$\red { The \: probability \:that \:the \:bulb \:is}$

$\red {not \: defective }\green {= P(E_{2})=\frac{15}{19}}$

Step-by-step explanation:

$i ) Let \: the \:event \: getting \: defective\:bulb \\is \:E_{1}.$

$n(E_{1}) = 4 , \: n(S) = 20$

$\therefore P(E_{1}) = \frac{n(E_{1})}{n(S)}\\=\frac{4}{20}\\= \frac{1}{5}$

$ii) After \:taking \:one \:bulb \:which \:is \:not \\defective \:there \:are \:19 \:bulbs$

$Let \:the \: event \: getting \:not \: defective\\bulb\:is \:E_{2}$

$n(E_{2}) = 15 , \: n(S) = 19$

$The \: probability \:that \:the \:bulb \:is \\not \: defective = P(E_{2})$

$\therefore P(E_{2}) = \frac{15}{19}$

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