Question

Two students are selected, without replacement from a group of 8 male and 5 female students. what is the probability exactly one female is selected?

Answer 1

sample space ={8 males + 5 females} = 13 
P(ONLY ONE FEMALE) = 5/13 = 0.384

Answer 2

The probability that exactly one female is selected is 0.513

The distribution of students is given as:

Male = 8

Female = 5

So, the sample size (n) is:

n = 8 + 5

n = 13

The probability that exactly one female is selected is represented as:

P = Male and Female or Female and Male

So, we have:

$P = \frac {8}{13} * \frac 5{12} + \frac {5}{13} * \frac 8{12}$

Rewrite as:

$P = 2 * \frac {5}{13} * \frac 8{12}$

Evaluate

$P =0.5128$

Hence, the probability that exactly one female is selected is 0.513

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