**Answer:**

(a) Expected gain = 30

(b) Standard deviation = 66.03

**Explanation:**

From the question, we are given the following:

Probability of loss = 10%

Loss amount = $150

Probability of Saving = 100% - Probability of loss = 100% - 10% = 90%

Saving amount = $50

Therefore, we proceed as follows:

**a) If she books the cheaper flight, what can she expect to gain, on average?**

This can be calculated as follows:

Expected gain = (Probability of loss * (-Loss amount)) + (Probability of Saving * Saving amount) = (10% * (-150)) + (90% * 50) = -15 + 45 = 30

**b) What is the standard deviation?**

Standard deviation can be described as a measure of the amount of variation a set of values. This can be calculated from the variance as follows:

Variance = (Probability of loss * (-Loss amount - Expected gain)^2) + (Probability of Saving * (Saving amount - Expected gain)^2) = (10% * (-150 - 50)^2) + (90% * (50 - 30)^2) = (10% * (-200)^2) + (90% * (20)^2) = (10% * 40,000) + (90% * 400) = 4,000 + 360 = 4,360

Standard deviation = Variance^0.5 = 4,360^0.5 = 66.03