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3 years ago

10

A class is made up of 10 boys and 4 girls. Half of the girls wear glasses. A student is selected at random from the class what i

s the probability that the student is a girl with glasses

2 answers:

ZanzabumX [31]3 years ago

8 0

Answer:

2/14 or 1/7

Step-by-step explanation:

Half the girls where glasses so 2 girls.

there are only 2 girls that wear glasses out of all the 14

so the answer is 2/14

NikAS [45]3 years ago

8 0

Answer:
1 in 6 chance or 16.6- percent chance (17% chance rounded up)

Explanation: So first of all the probability of a girl getting called in general is a 4 in 14 chance. Or a 25% chance. We can figure this out by finding out the amount of girls, and adding it by the guys, and putting the girls as the numerator. Since half the girls wear glasses, this puts it down to 2 girls in all, simply replace the 4 with a 2 and you have a 2 in 14 chance, which simplifies to a 1 in 6 chance. Thus, the probability would be a 1 in 6 chance, or 16.6- chance.

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Answer:

1. $P(s_1|I)=\frac{1}{11}$

2. $P(s_2|I)=\frac{8}{11}$

3. $P(s_3|I)=\frac{2}{11}$

Step-by-step explanation:

Given information:

$P(s_1)=0.1, P(s_2)=0.6, P(s_3)=0.3$

$P(I|s_1)=0.15,P(I|s_2)=0.2,P(I|s_3)=0.1$

(1)

We need to find the value of P(s₁|I).

$P(s_1|I)=\frac{P(I|s_1)P(s_1)}{P(I|s_1)P(s_1)+P(I|s_2)P(s_2)+P(I|s_3)P(s_3)}$

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Therefore the value of P(s₁|I) is $\frac{1}{11}$ .

(2)

We need to find the value of P(s₂|I).

$P(s_2|I)=\frac{P(I|s_2)P(s_2)}{P(I|s_1)P(s_1)+P(I|s_2)P(s_2)+P(I|s_3)P(s_3)}$

$P(s_2|I)=\frac{(0.2)(0.6)}{(0.15)(0.1)+(0.2)(0.6)+(0.1)(0.3)}$

$P(s_2|I)=\frac{0.12}{0.015+0.12+0.03}$

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$P(s_2|I)=\frac{8}{11}$

Therefore the value of P(s₂|I) is $\frac{8}{11}$ .

(3)

We need to find the value of P(s₃|I).

$P(s_3|I)=\frac{P(I|s_3)P(s_3)}{P(I|s_1)P(s_1)+P(I|s_2)P(s_2)+P(I|s_3)P(s_3)}$

$P(s_3|I)=\frac{(0.1)(0.3)}{(0.15)(0.1)+(0.2)(0.6)+(0.1)(0.3)}$

$P(s_3|I)=\frac{0.03}{0.015+0.12+0.03}$

$P(s_3|I)=\frac{0.03}{0.165}$

$P(s_3|I)=\frac{2}{11}$

Therefore the value of P(s₃|I) is $\frac{2}{11}$ .

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