Leaving Cert Mathematics Probability: There are 16 girls and 8 boys in

There are 16 girls and 8 boys in a class - Leaving Cert Mathematics - Question b - 2011

Question b

There are 16 girls and 8 boys in a class. Half of these 24 students study French. The probability that a randomly selected girl studies French is 1.5 times the proba... show full transcript

Worked Solution & Example Answer:There are 16 girls and 8 boys in a class - Leaving Cert Mathematics - Question b - 2011

Step 1

Let x = number of boys who study French.

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Answer

From the problem, let the number of boys studying French be represented as $x$ . Therefore, the number of girls studying French will be $12 - x$ because half of the total students (24) study French.

We know that the total girls are 16, so the expression for girls studying French becomes: $12 - x = \text{number of girls who study French}.$

The probability that a randomly selected girl studies French is: $P(G_F) = \frac{12 - x}{16}.$

The probability that a randomly selected boy studies French is: $P(B_F) = \frac{x}{8}.$

According to the problem, the relationship between these probabilities is given by: $P(G_F) = 1.5 imes P(B_F).$

Step 2

Set up the equation based on the probabilities.

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Answer

Substituting the probabilities into the equation: $\frac{12 - x}{16} = 1.5 \times \frac{x}{8}.$

To eliminate the fractions, multiply through by 16: $12 - x = 1.5 \times 2x$ $12 - x = 3x$

Rearranging gives: $12 = 4x$ $x = 3.$

Thus, the number of boys in the class who study French is 3.

There are 16 girls and 8 boys in a class - Leaving Cert Mathematics - Question b - 2011

Worked Solution & Example Answer:There are 16 girls and 8 boys in a class - Leaving Cert Mathematics - Question b - 2011

Let x = number of boys who study French.

Set up the equation based on the probabilities.

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