1. There are 4 airlines to travel south and 7 land lines. Find the probability of: a) Travel by plane b) Travel by bus AND plane

a) The probability of traveling by plane:
P(\text{plane}) = \frac{4 \text{ airlines}}{4 \text{ airlines} + 7 \text{ land lines}} = \frac{4}{11}

b) The probability of traveling by bus and then by plane:
1. Probability of traveling by plane:
P(\text{plane}) = \frac{4}{11}

2. Assuming there are 10 other choices (since choosing a plane will exclude one option from the total):
P(\text{bus}) = \frac{7 \text{ land lines}}{10 \text{ choices (11 choices - 1 plane chosen)}} = \frac{7}{10}

3. Combined probability:
P(\text{bus AND plane}) = P(\text{bus}) \times P(\text{plane}) = \frac{7}{10} \times \frac{4}{11} = \frac{28}{110} = \frac{14}{55}

Answer:
a)
\frac{4}{11}

b)
\frac{14}{55}