Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than 100 hours given that it is of type 1 is 0.7, and given that it is of type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is

0.55

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Solution

The correct option is A 0.55
Let A = {Bulb gives more than 100 hrs. service}

$E_{1} = {Bulb of Type of I}$

$E_{2} = {Bulb of Type of II}$

$Given, P (E_{1}) = 0.5$ & $P (A / E_{1}) = 0.7$
$P (E_{2}) = 0.5$ & $P (A / E_{2}) = 0.4$

By total probability,

$P (A) = P (E_{1}) P (A / E_{1}) + P (E_{2}) P (A / E_{2})$

$= 0.5 \times 0.7 + 0.5 \times 0.4 = 0.55$

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The correct option is A 0.55Let A = {Bulb gives more than 100 hrs. service} E1={Bulb of Type of I} E2={Bulb of Type of II} Given, P(E1)=0.5 & P(A/E1)=0.7 P(E2)=0.5 & P(A/E2)=0.4 By total probability, P(A)=P(E1)P(A/E1)+P(E2)P(A/E2) =0.5×0.7+0.5×0.4=0.55