My Approach:
If 100 are produced 2 light bulbs will be defective.
In 10 cases (10 lightbulbs each); we have a 50% chance that the 2 will be in 1 box and a 50% chance that 2 defectives will be in 2 boxes.
Therefore the probability of it failing its guarantee is (1/10)(1/2)= 5%
Is this correct? I am not sure how else to approach this problem.
Best Answer
Hint:$P(x \geq 2) = 1 - P(x < 2) = 1 - P(x = 0) - P(x = 1) = 1 - \binom{10}{0}(0.02)^0\cdot (0.98)^{10} - \binom{10}{1}(0.02)^1\cdot 0.98^{9}$. Can you work out the details?