Question

1. some children where asked about their holidays.

a) complete the table above.
one of the children is chosen. calculate the probability of
b) a child who stayed in a hotel.
a child who went to america is chosen. calculate the probability of
c) that they stayed in a tent.
d) that they did not stay in a villa.

Explanation:

Step1: Complete the table

• Europe - Caravan: \(22-(3 + 2+7)=10\)
• Japan - Hotel: \(13-(2 + 5)=6\)
• Japan - Caravan: \(11-(5 + 6+0)=0\)
• America - Villa: \(12-(3 + 5)=4\)
• America - Caravan: \((50-(22 + 11))-(4 + 5)=8\)
• America - Tent: \(10-(7 + 0)=3\)
• America - TOTAL: \(4 + 5+8 + 3=20\)
• Caravan - TOTAL: \(10+8 + 0=18\)

Step2: Probability of choosing a child who stayed in a hotel (part b)

The formula for probability is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
The number of children who stayed in a hotel is \(13\), and the total number of children is \(50\). So \(P=\frac{13}{50}\)

Step3: Probability that a child who went to America stayed in a tent (part c)

The number of children who went to America is \(20\), and the number of children who went to America and stayed in a tent is \(3\). So \(P=\frac{3}{20}\)

Step4: Probability that a child who went to America did not stay in a villa (part d)

The number of children who went to America is \(20\), and the number of children who went to America and stayed in a villa is \(4\). The number of children who went to America and did not stay in a villa is \(20 - 4=16\). So \(P=\frac{16}{20}=\frac{4}{5}\)

Answer:

a) The completed table:

	Villa	Hotel	Caravan	Tent	TOTAL
America	4	5	8	3	20
Japan	5	6	0	0	11
TOTAL	12	13	18	10	50

b) \(\frac{13}{50}\)
c) \(\frac{3}{20}\)
d) \(\frac{4}{5}\)