Question

Out of 100 person surveyed , 72 had a wallet, 85 wore shoes, 58 carried a briefcase, 98 wore a ring.how many person must have had at least all four items?

Answer 1

There are many ways to answer this question. But I am giving a logical answer instead of using any formulas.

The question says that there were a total of 100 people. So, we need to calculate first how many people out of 100 did not those things.

People who did not have a wallet = 100 - 72 = 28.

People who did not wear shoes = 100 - 85 = 15.

People who did not carry a suitcase = 100 - 58 = 42.

People who did not wear a ring = 100 - 98 = 2.

So, the sum of these gives = 28 + 15 + 42 + 2 = 87.

So, 87 people out of 100 did not have at least one of these things.

So, 100 - 87 = 13. Thus, at least 13 people had all these 4 things.

Answer 2

For us to solve this question, we should use the concept of probability.

Probability = Number of outcomes/total number of possible outcomes.

In this case we use number of people.

PROBABILITIES :

Having a wallet = 72/100=0.72

Wearing shoes = 85/100=0.85

Carrying a briefcase = 58/100=0.58

Wearing a ring= 98/100=0.98

Probability that one has at least all items - This means that this person must have all the four items.

That is: Has a ring and a wallet and a briefcase and is wearing shoes.

The and means we multiply the probabilities since it is a conditional probability.

Therefore the probability is:

0.72×0.85×0.58×0.98=0.3478608

Rounding off to 2 decimal places we get:

0.35

The total number of people is 100 therefore 0.35 is equivalent to :

0.35×100=35 people

Ans=35 people.