Question

A survey was done on 250 buyers of a brand 'X' to study how many were first time buyers and how many were repeat buyers. Out of the 130 male buyers, 60 were first time buyers of the brand and out of the 120 female buyers, 76 were repeat buyers of the brand. If a customer is to be chosen at random, calculate the following probabilities: a. Probability that the customer will be male. b. Probability that the customer will be a first-time buyer given that the customer is female. c. Probability that the customer will be female given that the customer is a repeat customer. d. Probability that the customer is both male and a repeat customer.

Answer 1

Total number of buyers = 250

Male buyers = 130

First time buyers = 60

Repeated buyers

= 130 - 60

= 70

Female buyers = 120

Repeated buyers = 76

First time buyers

= 120 - 76

= 44

____________________________

(i) p(selected customer will be a male)

= total male buyers/total no. of buyers

= 130/250

= 13/25

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(ii) p(selected customer will be a first time female buyer)

= total first time female buyers/total no. of buyers

= 44/250

= 22/125

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(ii) p(selected customer is a repeated female buyer)

= total repeated female buyers/total no. of buyers

= 76/250

= 38/125

----------------

(iii) p(selected customer is a repeated male buyer)

= total male repeated buyers/total no. of buyers

= 70/250

= 35/125

= 7/25

Answer 2

$</p><p>\tt{\huge{\pink{Hello!!! }}}$

$</p><p>\tt{\red{Given \: - }}$

• Total number of buyers = 250

• Male buyers = 130

• First time buyers = 60

• Repeated buyers = 130 - 60 = 70

• Female buyers = 120

• Repeated buyers = 76

• First time buyers = 120 - 76 = 44

___________

$</p><p>\tt{\orange {\huge{\boxed {\boxed {Solution \: - }}}}}$

$\tt{ \implies{\purple{P_ {a} \: = \dfrac{13}{25 } }}}$

$\tt{ \implies{\purple{P_ {b} \: = \dfrac{22}{125 } }}}$

$\tt{\implies{ \purple{P_{c} \: = \dfrac{38}{125 }} }}$

$\tt{ \implies{\purple{P_{d} \: = \dfrac{7}{25 } }}}$