Question

How do u get the answer to the question below?

Answer 1

Step-by-step explanation:

Given;

We are told that a chorus has 50 girls and 35 boys. Two of the choir members is to be chosen at random.

Required;

Calculate the probability that both members chosen will be boys.

Step-by-step solution;

First thing to note is the formula for calculating the probability of an event.

The formula used in calculating this is given as;

`P[E]=\frac{Number\text{ }of\text{ }required\text{ }outcomes}{Number\text{ }of\text{ }all\text{ }possible\text{ }outcomes}`

For this experiment, the total number of all possible outcomes is 85, that is, 50 girls plus 35 boys.

Also, the number of required outcomes is 35, that is, number of boys.

This means the probability of selecting a boy when a chorus member is chosen at random will be;

`\begin{gathered} P[Boy]=(35)/(85) \\ \\ P[Boy]=(7)/(17) \end{gathered}`

However, the probability that both will be boys means the probability of event A and event B. This is a product of probabilities. That is;

`P[A]\text{ }and\text{ }P[B]=A* B`

Note that in this case, both events are the same, that is, the probability of choosing a boy;

`\begin{gathered} P[A]=(7)/(17) \\ \\ Also; \\ \\ P[B]=(7)/(17) \end{gathered}`

Therefore;

`\begin{gathered} P[A]\text{ }and\text{ }P[B]=(7)/(17)*(7)/(17) \\ \\ P[A]\text{ }and\text{ }P[B]=(49)/(289) \end{gathered}`

ANSWER:

Option E is the correct answer,

`(49)/(289)`