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Probability — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsProbability4 Marks
Question
The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English Examination is 0.75. What is the probability of passing the Hindi Examination?
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Answer

Let E be the event that student passed in english examination
$\therefore\text{P}(\text{E})=0.75$
Let H be the event that student passed in hindi examination
$\therefore\text{P}(\text{H})=?$
Also, $\text{P}(\text{E}\cap\text{H})=0.5$ and $\text{P}(\overline{\text{E}\cap\text{H}})=0.1$
$\because\text{P}(\overline{\text{E}}\cap\overline{\text{H}})=1-\text{P}(\text{E}\cup\text{H})$
$\Rightarrow\text{P}({\text{E}}\cup{\text{H}})=1-0.1$
$=0.9$
Now,
$\text{P}({\text{E}}\cup{\text{H}})=\text{P}(\text{E})+\text{P}(\text{H})-\text{P}({\text{E}}\cap{\text{H}})$
$0.9=0.75+\text{P}(\text{H})-0.5$
$\text{P}(\text{H})=0.90-0.25$
$=0.65$

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