A flashlight has 8 batteries out of which 3 are dead. If two batteries are selected at random and tested, the probability that both are dead is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{3}{28} \)
Two batteries are chosen from 8, and both must come from the 3 dead ones:
\( \displaystyle P(\text{both dead})=\frac{{}^{3}C_{2}}{{}^{8}C_{2}} \)
\( \displaystyle =\frac{3}{28} \)
Tip: Two batteries are taken out together, so the selection is without replacement. \( \left(\frac{3}{8}\right)^{2}=\frac{9}{64} \) (Option 3) is the with-replacement value.
NCERT Exemplar:
Probability
