in a class of 60 boys and 40 girls, it is observed tha 24 boys and 21 girls wear glasses. what is the probability that: (1)A student is picked at random from this calss wear glasses (2)A girl picked at random does not wear glsses.(3)A boy pivked at random wear glsses.(4)A student picked at random either a boy who wear glasses or a girl who does not wear glasses
boys wearing glasses = 24
boys not wearing glasses = 36
girls wearing glasses = 21
girls not wearing glasses = 19
1) prob(a student wears glasses) = 45/100= 9/20
2) 19/40
3) ...
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(1) The probability that a student wears glasses can be calculated by adding the probability of picking a boy who wears glasses and the probability of picking a girl who wears glasses, and dividing it by the total number of students:
Number of boys wearing glasses: 24
Number of girls wearing glasses: 21
Total number of students: 60 + 40 = 100
P(student wears glasses) = (24 + 21) / 100 = 45/100 = 9/20
So the probability that a student picked at random from this class wears glasses is 9/20.
(2) The probability that a girl picked at random does not wear glasses can be calculated by subtracting the probability of picking a girl who wears glasses from 1:
Number of girls wearing glasses: 21
Total number of girls: 40
P(girl does not wear glasses) = 1 - (21/40) = 19/40
So the probability that a girl picked at random from this class does not wear glasses is 19/40.
(3) The probability that a boy picked at random wears glasses can be calculated by dividing the number of boys wearing glasses by the total number of boys:
Number of boys wearing glasses: 24
Total number of boys: 60
P(boy wears glasses) = 24/60 = 2/5
So the probability that a boy picked at random from this class wears glasses is 2/5.
(4) The probability that a student picked at random is either a boy who wears glasses or a girl who does not wear glasses can be calculated by adding the probabilities of these two events:
P(boy wearing glasses OR girl not wearing glasses) = P(boy wearing glasses) + P(girl not wearing glasses)
P(boy wearing glasses OR girl not wearing glasses) = (24/100) + (19/40) = (12/50) + (19/40) = 24/100 + 38/100 = 62/100 = 31/50
So the probability that a student picked at random from this class is either a boy who wears glasses or a girl who does not wear glasses is 31/50.
To find the probability, we can use the formula:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Let's solve each part of the question step by step:
(1) Probability that a student picked at random from this class wears glasses:
Number of boys wearing glasses = 24
Number of girls wearing glasses = 21
Total number of students wearing glasses = 24 (boys) + 21 (girls) = 45
Total number of students in the class = 60 (boys) + 40 (girls) = 100
Probability = Number of students wearing glasses / Total number of students
= 45 / 100
= 0.45 (or 45%)
Therefore, the probability that a student picked at random from this class wears glasses is 0.45 or 45%.
(2) Probability that a girl picked at random does not wear glasses:
Number of girls wearing glasses = 21
Total number of girls in the class = 40
Number of girls not wearing glasses = Total number of girls - Number of girls wearing glasses
= 40 - 21
= 19
Probability = Number of girls not wearing glasses / Total number of girls
= 19 / 40
= 0.475 (or 47.5%)
Therefore, the probability that a girl picked at random from this class does not wear glasses is 0.475 or 47.5%.
(3) Probability that a boy picked at random wears glasses:
Number of boys wearing glasses = 24
Total number of boys in the class = 60
Probability = Number of boys wearing glasses / Total number of boys
= 24 / 60
= 0.4 (or 40%)
Therefore, the probability that a boy picked at random from this class wears glasses is 0.4 or 40%.
(4) Probability that a student picked at random is either a boy who wears glasses or a girl who does not wear glasses:
Number of boys wearing glasses = 24
Number of girls not wearing glasses = 19
Total number of students in the class = 100
Number of students satisfying the condition = Number of boys wearing glasses + Number of girls not wearing glasses
= 24 + 19
= 43
Probability = Number of students satisfying the condition / Total number of students
= 43 / 100
= 0.43 (or 43%)
Therefore, the probability that a student picked at random from this class is either a boy who wears glasses or a girl who does not wear glasses is 0.43 or 43%.
To find the probabilities in this scenario, we need to calculate the ratios of the desired outcomes to the total number of possibilities.
Given information:
- Total number of students = 60 boys + 40 girls = 100 students
- Number of boys who wear glasses = 24
- Number of girls who wear glasses = 21
Let's calculate the probabilities:
(1) The probability that a student, selected randomly from the class, wears glasses:
Total number of students who wear glasses = 24 boys + 21 girls = 45 students
P(student wears glasses) = Number of students who wear glasses / Total number of students
= 45/100
= 0.45
= 45%
(2) The probability that a girl, selected randomly, does not wear glasses:
Number of girls who do not wear glasses = Total number of girls - Number of girls who wear glasses = 40 - 21 = 19 girls
P(girl does not wear glasses) = Number of girls who do not wear glasses / Total number of students
= 19/100
= 0.19
= 19%
(3) The probability that a boy, selected randomly, wears glasses:
P(boy wears glasses) = Number of boys who wear glasses / Total number of students
= 24/100
= 0.24
= 24%
(4) The probability that a student, selected randomly, is either a boy who wears glasses or a girl who does not wear glasses:
Number of boys who wear glasses + Number of girls who do not wear glasses = 24 + 19 = 43 students
P(student is either a boy who wears glasses or a girl who does not wear glasses) = Number of students who satisfy this condition / Total number of students
= 43/100
= 0.43
= 43%
So, the probability is 45% that a student picked at random wears glasses, 19% that a girl picked randomly does not wear glasses, 24% that a boy picked randomly wears glasses, and 43% that a student picked randomly is either a boy who wears glasses or a girl who does not wear glasses.