1500 families were surveyed and following data was recorded about their maids at homes. Type of maids|Only part time|Only full time|Both|
Number of families|860 | 370 | 250 |
A family is selected at random. Find the probability that the family selected has
(i)Both types of maids (ii) Part time maids (iii)No maids

Explanation:-

Total number of families are surveyed = 1500

Total number of possible outcomes = 1500

Number of part time maids = 860

Number of favourable outcomes to part time maids = 860

Number of only full time maids = 370

Number of favourable outcomes to only full time maids = 370

Number of both type of maids = 250

Number of favourable outcomes to both type of maids = 250

From all families selecting a family randomly is an event then

We know that

Probability of an event =

Number of favourable outcomes/Total number of possible outcomes

1⟩ Probability of getting both type of maids

⇛250/1500

⇛25/150

⇛1/6

Probability of a family has both type of maids= 1/6.

2⟩ Probability of getting Part time maids

= 860/1500

⇛86/150

⇛43/125

Probability of getting Part time maids = 43/125.

3⟩. Number of part time maids =n(P only )=860

Number of only full time maids =n(F only) = 370

Number of both type of maids = n(PnF)= 250

Total number of families are surveyed= n(PUF)

= 1500

number of no maids =

n(PUF)= n(only P)+n(only F)+n(PnF)

= 1500-(860+370+250)

⇛1500-(1480)

⇛20

Number of no maids = 20

Probability of getting no maid = 20/1500

⇛2/150

⇛1/125

Probability of getting no maid = 1/125.

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