Video: CBSE Class X • Pack 2 • 2017 • Question 4

CBSE Class X • Pack 2 • 2017 • Question 4

02:41

Video Transcript

The probability of randomly selecting a rotten apple from a heap of 900 apples is 0.18. What is the number of rotten apples in the heap?

We have a heap of apples, and we randomly select one. That means that each apple is equally likely to be picked. When we’re dealing with equally likely outcomes, the probability of a given event is a fraction. The denominator of the fraction is the total number of equally likely outcomes. And the numerator is the number of those equally likely outcomes that are favourable, that is, that are part of the event.

In our question, the event is selecting a rotten apple. And as each apple is equally likely to be selected, the total number of equally likely outcomes is the total number of apples. And the number of the favorable outcomes is the number of these equally likely apples which are rotten. So now what?

Well, we’re told in the question that the probability of randomly selecting a rotten apple is 0.18. So we substitute this value into our equation. We’re also told that the total number of apples in the heap is 900. So we see that 0.18 is the number of rotten apples over 900. Multiplying both sides of the equation by 900, we see that 900 times 0.18 is the number of rotten apples that we’re looking for.

Now we just need to perform this multiplication, and you can do that in whichever way you’d like. I’m going to use the fact that 900 is nine times 100, and I’m going to give that 100 to the 0.18. 100 times 0.18 is 18. So we have nine times 18, and we can multiply these in the normal way. Nine times eight is 72. We write the digit zero and then perform nine times one, to get nine. And then we add 72 and 90. Two plus zero is two, and seven plus nine is 16. There are therefore 162 rotten apples in the heap.

You should check that this number makes sense. 162 is just under a fifth of the 900 apples. And the probability is indeed just under a fifth. So it seems to be a reasonable answer.

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