H2 maths probability

quailmaster SG

John has 90 unlabelled cans in a box. Of the 90 cans 24 contain baby corn, 12contain beans, 36 contain peas and 18 contain mushrooms.

Find the probability that John will have to open more than 2 cans before he finds one which does not contain baby corn.

revetandem SG

Probability that 1st can he opens contains baby corn=24/90=4/15

Probability that 1st can he opens is non-baby corn but second one contains baby corn=66/90*24/89=88/445

Thus, Probability that he needs to open more than 2 cans before he finds one which does not contain baby corn =1-4/15-88/445=143/267

Alternatively, you can think of it this way:

Probablility that first 2 cans opened are non baby corn=66/90*65/89=143/267. Same result.

revetandem SG

Oh sorry interpreted the question wrongly.

Probablility should be 24/90*23/89=92/1335

TrueHeart SG

John has 90 unlabelled cans in a box. Of the 90 cans 24 contain baby corn, 12contain beans, 36 contain peas and 18 contain mushrooms.

Find the probability that John will have to open more than 2 cans before he finds one which does not contain baby corn.

Hi quailmaster,

Let us have a look at this question step-by-step.

Firstly, let us consider the probability of getting a can of baby corn on John's first try. That will be 24/90.

Next, let us consider the probability of getting a can of baby corns on John's second try. That will be 66/90 X 24/89 = 88/445

Thus, the probability of John getting a can of baby corns on his first two tries will be 24/90 + 88/445 = 124/267

Hence, the probability of John taking more than two tries will be 1 - 124/267 = 143/267

Cheers.

revetandem SG

Apologies for making the wrong answer... never think through properly.

wee_ws SG

Hi,

From this question, a good lesson to be learnt is to consider complementary events.

Thanks.

Cheers,
Wen Shih

wee_ws SG

Hi,

In addition, both addition and multiplication principles we have encountered in P&C still apply in the topic of probability. Recall that the addition principle is used for mutually exclusive cases and the multiplication principle is used to deal with independent events.

One should also take note of notions of conditional probability, probability tree, Venn diagram and table of outcomes (where cases are listed out systematically).

Hope these pointers will benefit students learning this topic :)

Cheers,
Wen Shih