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Mrs.harper is randomly selecting 4 students to give their presentations today. if there 16 boys and 14 girls in the class, what is the probability that the first two students selected are girls and the next two are boys

Respuesta :

jorel1380
Since these students are picked in order, we have:
14/30x13/29x16/28x15/27=0.06226053639846743295019157088123 probability of choosing students as stated. ☺☺☺☺

Answer:

Givens

  • There are 16 boys and 14 girls.

The probability we are gonna use here is the standard probability, which is defined as the quotient between the number of events and the number of total outcomes.

So, the probability to select a girl is

[tex]P_{girl} =\frac{14}{30}=\frac{7}{15}[/tex]

Now, the probability to selec a girl as second choice is

[tex]P_{girl}=\frac{13}{29}[/tex]

But, the problem asks for the probability where the first two students selected are girls, that means they are being picked at the same time, so

[tex]P_{girl}=\frac{7}{15} \times \frac{13}{29} =\frac{91}{435} \approx 0.27[/tex]

Therefore, the probability where the first two students are girls is around 27%.

Then, we do the same process for boys, but, notice that the total outcomes must decrease, because we already chose 2 students

[tex]P_{boy}=\frac{16}{28} \times \frac{15}{27}=\frac{240}{756} \approx 0.32[/tex]

Therefore, the probability where the next two students are boys is around 32%.