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Question

On a certain day the chance of rain is $$80\%$$ in Delhi and $$30\%$$ in Hyderabad. Assume that the chance of rain in the two cities is independent. What is the probability that it will not rain in either city?


A
7%
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B
14%
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C
24%
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D
50%
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Solution

The correct option is D $$14\%$$
Probability that it will not rain in Delhi $$= 100\% – 80\%$$ 
                                                      $$ = 20\%  = 0.2$$
Probability that it will not rain in Hyderabad $$= 100\% – 30\% $$
                                                                  $$= 70\%  = 0.7$$
Since the chances of rain in both cities is independent
$$\therefore$$ Probability that it will not rain in either city $$=0.2 \times 0.7$$
                                                                           $$= 0.14$$
$$\therefore$$ Probability that it will not rain in either city $$=14\%$$

Mathematics

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