Question

Question: Determine whether the scenario is independent or dependent. Calculate the probability. Mr. Tindel will randomly Selects two students from his class as the student council representatives There are 17 girls and 6 boys in his class. what is the probability Mr. Tindel will select two girls?

Answer 1

The probability of selecting two girs from the group is given by:

$P(girl1)\times P(girl2)$

The probability of selecting a girl first, is given by the division between the amount of girls in the class by the total number of people in the class.

• Number of girls in the class: ,17

,

• Total number of people: 17 girls+6boys=,23 ,people

Probability of selecting first a girl:

$P(girl1)=\frac{17}{23}$

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Now we calculate the probability that, after selecting a girl, we select another girl in the second place. Again we need the total number of girls:

• Number of girls available for selecting: ,16

We substract 1 girl from the total because we already select one girl in the first place.

For this same reason, the total number of people in the class will also decrease by 1:

• Total number of people: ,22

And thus, the probability of selecting a girl in the second place is:

$\frac{16}{22}=\frac{8}{11}$

Finally, as stated at the beginning, we multiply both probabilities to find the probability Mr. Tindel will select two girls:

$P(girl1)\times P(girl2)=\frac{17}{23}\times\frac{8}{11}=\frac{17\times8}{23\times11}=\frac{136}{253}$

which in percentage is:

$\frac{136}{253}=0.537$

53.7%

Determine whether the scenario is independent or dependent:

The scenario is dependent, because the second probability depends on the result of the first event.