Answer to Question #191761 in Statistics and Probability for maria

Question

Monthly spending ($)

 

 

 

 

 

 

Age

20s

30s

$0.00 - $49.99

75

29

$50.00 - $99.99

91

83

$100.00 - $149.99

113

90

$150.00 - $199.99

89

128

$200.00 - $249.99

63

159

$250.00 or more

34

46

Total customers

465

535

 

a. What is the probability that a customer spends at least $150.00 or is in his/her 30s?

Answer 1

The table of this question will be:

Ages

$$\def\arraystretch{1.5} \begin{array}{c:c:c} Monthly\ spending(\$) & 20s & 30s \\ \hline 0.00\$-49.99\$ & 75 & 29\\ 50.00\$-99.99\$ & 91& 83\\ 100.00\$-149.99\$ & 113 & 90 \\ 150.00\$-199.99\$ & 89 & 128\\ 200.00\$-249.99\$ & 63 & 159\\ 250.00\$ \ or\ more & 34 & 46\\ \hdashline \text{Total customers} & 465 & 535 \end{array}$$

The probability that a customer spends at least $150.00 or is in his/her 30s will be

$$P\big((\geq150.00\$)\cup(30s)\big)$$

$$=\dfrac{535}{465+535}+\dfrac{89+63+34}{465+535}=0.721$$

The probability that a customer spends at least $150.00 or is in his/her 30s is $0.721.$