Question

A box contains 50 bolts and 150 nuts. On checking the box ,it was found that half of the bolts and half of the nuts are rusted. If one item is chosen at random, find the probability that it is rusted.

Answer 1

Answer:

Total number of nuts and bolts in the box = 150 + 50 = 200

Number of nuts and bolts rusted = 1 / 2 × 200 = 100

P(a rusted nut or bolt) = 100 / 200 = 1 / 2

Step-by-step explanation:

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Answer 2

Given: A box contains 50 bolts and 150 nuts. On checking the box ,it was found that half of the bolts and half of the nuts are rusted.

To find: If one item is chosen at random, find the probability that it is rusted.

Solution:

According to the question, half the bolts are rusted so the number of rusted bolts is

$\frac{50}{2} = 25$

Similarly, the number of rusted nuts is calculated as follows.

$\frac{150}{2} = 75$

Now, the total number of nuts and bolts in the box is

$150 + 50 = 200$

And the number of rusted nuts and bolts in the box is

$25+75=100$

In order to find the probability of choosing an item from the box which is rusted is calculated by dividing the number of rusted items by the total number of items.

$P(E) = \frac{100}{200}$

         $= \frac{1}{2}$

Therefore, the probability that it is rusted is 1/2.