Question

a photography student took portrait photos of people from his hometown. he wants to develop 19 of the photos, 7 of which were of teenagers and 7 of which were of adults. if he randomly chooses to develop 4 of the photos in black and white in a specific order, what is the probability that the first 2 photos are of teenagers and the last 2 are of adults? write your answer as a decimal rounded to four decimal places.

Explanation:

Step1: Calculate probability of first - teenager photo

The total number of photos to develop is $n = 19$, and the number of teenager photos is $m_1=7$. The probability that the first photo is of a teenager is $P_1=\frac{7}{19}$.

Step2: Calculate probability of second - teenager photo

After choosing the first teenager photo, there are $n_1 = 18$ photos left and $m_2 = 6$ teenager photos left. So the probability that the second photo is of a teenager is $P_2=\frac{6}{18}$.

Step3: Calculate probability of first - adult photo

After choosing 2 teenager photos, there are $n_2=17$ photos left and the number of adult photos is $m_3 = 7$. So the probability that the third photo is of an adult is $P_3=\frac{7}{17}$.

Step4: Calculate probability of second - adult photo

After choosing 3 photos, there are $n_3 = 16$ photos left and $m_4=6$ adult photos left. So the probability that the fourth photo is of an adult is $P_4=\frac{6}{16}$.

Step5: Calculate the overall probability

Since these are independent - sequential events, the overall probability $P = P_1\times P_2\times P_3\times P_4$.
$P=\frac{7}{19}\times\frac{6}{18}\times\frac{7}{17}\times\frac{6}{16}=\frac{7\times6\times7\times6}{19\times18\times17\times16}=\frac{1764}{93024}\approx0.0189$.

Answer:

$0.0189$