Answer:
1) Probability(All components function properly) = 2/13 = 0.1538
2) P(Exactly 2 are defective) = 30/91 = 0.3297
3) P(X≥1) = 0.8461
f) none of the above
Explanation:
Total electrical components = 14
Components not functioning properly = 3
Components functioning properly = 14-3 = 11
Components selected = 6
1) If all selected components are functioning properly, that means all the 6 components were selected from the 11 components which were functioning properly so,
No. of ways to select components functioning properly = ¹¹C₆
Total no. of ways to select 6 components out of 14 = ¹⁴C₆
Probability(All components function properly) = No. of ways to select components functioning properly/Total no. of ways to select 6 components out of 14
= ¹¹C₆ / ¹⁴C₆
= 462/3003
Probability(All components function properly) = 2/13 = 0.1538
2) P(Exactly 2 are defective) can be calculated by considering that 2 are selected out of the 3 defective components and rest of the 4 components are selected from the pool of 11 components which are not defective.
P(Exactly 2 are defective) = ³C₂ ¹¹C₄ / ¹⁴C₆
= (3 x 330)/3003
P(Exactly 2 are defective) = 30/91 = 0.3297
3) Now we need to calculate the probability P(X≥1). The simple way to calculate this probability is:
P(X≥1) = 1 - P(X<1)
= 1 - P(X=0)
P(X=0) means no components are defective i.e. all components function properly. We have calculated this probability in part 1 so,
P(X≥1) = 1 - (2/13)
P(X≥1) = 0.8461
Since the answers to parts 1,2 and 3 do not match any of the options given here, the correct option is f) none of the above.