Question

In an exam, two reasoning problems, 1 and 2. are asked. 35% of students solved problem 1 and
15% students solved both the problems. How many students who solved the first problem will
also solve the second one?​

Answer 1

Answer:

80 %

Step-by-step explanation:

Here if 35% solve the first one and 15% solve both.

Then the student remaining are those who solved the 2nd problem only.

Now, the student who solved the 1 st as well as the 2nd are that common student ( who solved the 1st and 2nd both) + the student who solved only 2nd problem which is = 15 + 65 = 80.

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Answer 2

42.86% students who solved the first problem will  also solve the second one.

Explanation:

Let F = Number of students solved problem 1

S=  Number of students solved problem 2

As per given , we have

Probability that students solved problem 1 = P(F) =0.35

Probability that students solved both the problems = P(F∩S) =0.15

Using conditional probability ,

Probability that the students who solved the first problem will  also solve the second one :

$P(S|F)=\dfrac{P(F\cap S)}{P(S)}\\\\=\dfrac{0.15}{0.35}=\dfrac{15}{35}\\\\=\dfrac{3}{7}$

In percent , $\dfrac{3}{7}\times100\%=42.86\%$

Hence, 42.86% students who solved the first problem will  also solve the second one.

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