Question

1. an electrical store records the following information.

under 21 21 - 45 over 45 total
satellite 48 19 90
terrestrial 28 60
cable 86
total 97 116 300
a) complete the table above.
one of the records is chosen. calculate the probability of choosing
b) someone under 21 with cable.
an over 45 person is chosen. calculate the probability of
c) them not having cable.

Explanation:

Step1: Complete the table

• For Satellite \(21 - 45\) age - group: \(90-(48 + 19)=23\)
• For Terrestrial \(21 - 45\) age - group: \(60-(28 + x)\), and total \(21 - 45\) age - group: \(300-(97 + 116)=87\). Let the number of Terrestrial in \(21 - 45\) be \(y\). Then \(y=87-(23 + z)\) (where \(z\) is Cable in \(21 - 45\)). Also, for Terrestrial over \(45\): \(60-(28 + y)\). Since total Terrestrial is \(60\), and total over \(45\) is \(116\), number of Terrestrial over \(45\) is \(116-(19 + 86)=11\). Then \(y = 60-(28 + 11)=21\)
• For Cable under \(21\): \(97-(48 + 28)=21\)
• For Cable \(21 - 45\): \(87-(23 + 21)=43\)
• For Cable total: \(21+43 + 86=150\)
• For Terrestrial total: \(60\)
• For Satellite total: \(90\)
• For total \(21 - 45\): \(87\)

Step2: Probability of choosing someone under 21 with cable (part b)

The formula for probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). The number of people under 21 with cable is \(21\), and the total number of records is \(300\). So \(P=\frac{21}{300}=\frac{7}{100}=0.07\)

Step3: Probability of over 45 not having cable (part c)

The number of over - 45 people is \(116\). The number of over - 45 people not having cable is \(19 + 11=30\). Using the probability formula \(P=\frac{30}{116}=\frac{15}{58}\approx0.259\)

Answer:

a)

	Under 21	21 - 45	Over 45	TOTAL
Terrestrial	28	21	11	60
Cable	21	43	86	150
TOTAL	97	87	116	300

b) The probability of choosing someone under 21 with cable is \(\frac{7}{100}\)

c) The probability of an over - 45 person not having cable is \(\frac{15}{58}\)