Jagran Science Olympiad

My Sister today gave an exam in which she did't have the answer of any question.

Moreover each question was of 1 marks and if she got wrong there was a negative marking of -1/2 . If there were 60 questions in all and she attempted every question then what is the probability that she will pass that exam.

Passing marks is 60%.

Note: I Do not know the answer so I am posting it as a POST

#Probability

Easy Math Editor

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`2 \times 3`	$2 \times 3$
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Comments

She will pass the examination only if by chance the questions she has attempted will turn out to be correct. Otherwise her true marks are -30.

Sanjay Sahni - 7 years, 4 months ago

At least she must answer 44 questions right

Nadya Bachtiar - 7 years, 4 months ago

Assuming the chance of getting a question right to be $\frac{1}{2}$ .

Let the number of the questions solved correctly be $n$ . Then number of question solved incorrectly is $60 - n$

Therefore $n*1 - \frac{1}{2}(60 - n) \geq 36$

$\frac{3n}{2} - 30 \geq 36$

$\frac{3n}{2} \geq 66$

$n \geq 44$

Construct a string of length 60 made up of 1s and 0s. Then, assuming each 1 to be a right answer and each 0 to be a wrong answer, we see that each string corresponds to a way she could have give the test.

Number of ways she could have passed is Combination of strings with 16 0s, 15 0s, etc.

Total number of ways she could have answered = $2^ {60}$

Therefore probability = $\dfrac{{60 \choose 16} + {60 \choose 15} + \ldots + {60 \choose 0}}{2^{60}}$

Sadly, I can't find a way to simplify it.

Are you talking about the Dainik Jagran Science Olympiad? How were the questions?

Siddhartha Srivastava - 7 years, 4 months ago

Very nice............ Time was lesss Maths and phy were easy but There was no time to see Che and Bio..........

Anand Raj - 7 years, 4 months ago

This question is really a very good one. Did u take up this exam? Did this come in that exam? What award did you get in this exam?? What resources do you use to study? (just curious...:) ) @Anand Raj

Krishna Ar - 7 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$