Questions: You take a survey of your classmates' birthday months. A student is chosen at random. Find the probability of each event. (Enter your probabilities as fractions.) Month Number of students Month Number of students --- --- --- --- January 0 July 4 February 3 August 2 March 5 September 0 April 2 October 3 May 5 November 4 June 1 December 6 (a) The student was born in July. (b) The student was born in March. (c) The student was born in one of the last 3 months of the year.

Solution Steps

To find the total number of students surveyed, we sum the number of students born in each month:

$$\text{Total Students} = 0 + 3 + 5 + 2 + 5 + 1 + 4 + 2 + 0 + 3 + 4 + 6 = 35$$

The number of students born in July is 4. Therefore, the probability $P(\text{July})$ is calculated as follows:

$$P(\text{July}) = \frac{\text{Number of students born in July}}{\text{Total Students}} = \frac{4}{35}$$

The number of students born in March is 5. Thus, the probability $P(\text{March})$ is:

$$P(\text{March}) = \frac{\text{Number of students born in March}}{\text{Total Students}} = \frac{5}{35} = \frac{1}{7}$$

The number of students born in October, November, and December is:

$$\text{Students in last three months} = 3 + 4 + 6 = 13$$

The probability $P(\text{Last 3 Months})$ is then:

$$P(\text{Last 3 Months}) = \frac{\text{Number of students in last three months}}{\text{Total Students}} = \frac{13}{35}$$

Final Answer