Suppose a math class contains 31 students, 14 females (four of whom speak French) and 17 males (two of whom speak French). Compute the probability that a randomly selected student is female, given that the student speaks French.
To compute the probability that a randomly selected student is female, given that the student speaks French, we need to find the number of females who speak French and divide it by the total number of students who speak French.
Let's break down the information given:
Total number of students in the class = 31
Number of females = 14
Number of females who speak French = 4
Number of males = 17
Number of males who speak French = 2
Now, let's calculate the probability:
First, we need to find the total number of students who speak French, which is the sum of females who speak French and males who speak French.
Total number of students who speak French = number of females who speak French + number of males who speak French = 4 + 2 = 6 students.
Next, we want to find the probability that a randomly selected student is female, given that the student speaks French. We can use conditional probability to calculate this.
Conditional probability (probability of being female given that they speak French) = Probability of being female and speaking French / Probability of speaking French
Probability of being female and speaking French = Number of females who speak French = 4
Probability of speaking French = Total number of students who speak French = 6
Therefore, the probability that a randomly selected student is female, given that the student speaks French is:
4/6, which simplifies to 2/3 or 0.6667 (rounded to four decimal places).
So, the probability is 2/3 or 0.6667.