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In a class, there are 18 girls and 16 boys. The class teacher wants to choose one pupil for class monitor. What she does, she writes the name of each pupil on a card and puts them into a basket and mixes thoroughly. A child is asked to pick one card from the basket. What is the probability that the name written on the card is:
(i) The name of a girl (ii) The name of a boy?
In a class, there are 18 girls and 16 boys. The class teacher wants to choose one pupil for class monitor. What she does, she writes the name of each pupil on a card and puts them into a basket and mixes thoroughly. A child is asked to pick one card from the basket. What is the probability that the name written on the card is:
(i) The name of a girl (ii) The name of a boy?
Given: In a class there are 18 girls and 16 boys, the class teacher wants to choose one name. The class teacher writes all pupils’ name on a card and puts them in basket and mixes well thoroughly. A child picks one card
Required to find: The probability that the name written on the card is
(i) The name of a girl
(ii) The name of a boy
Total number of students in the class = 18 + 16 = 34
(i) The names of a girl are 18, so the number of favourable cases is 18
We know that, Probability = Number of favourable outcomes/ Total number of outcomes
Thus, the probability of getting a name of girl on the card = 18/34 = 9/17
(ii) The names of a boy are 16, so the number of favourable cases is 16
We know that, Probability = Number of favourable outcomes/ Total number of outcomes
Thus, the probability of getting a name of boy on the card = 16/34 = 8/17
(i) Total number of elementary events = total number of girls and boys = 18 + 16 =34
`therefore “Probability that the name written on the card is the name of a girl “=(“Favourable number of elementary events”)/(“Total number of elementary events”)=(18)/(34)=(9)/(17)`
(ii) Probability that the name written on the card is the name of a boy `=(“Favourable number of elemantary events”)/(“Total number of elementary events”)=(16)/(34)=(18)/(17)`
(iii) Topper of class is only one particular student.
`therefore` Favourable number of elementary event = 1
`therefore “Required probability “=(“Favourable number of elementry events”)/(“Total number of elementary events”)=(1)/(34)`
(iv) We do not want that name written on the card is Shiv Kumar. So, name written on the card may be of any other student except Shiv Kumar.
`therefore` Favourable number of elementary events = 33
`therefore “Required probability “=(33)/(34)`
Total no. of possible outcomes = 34 (18 girls, 16 boys)
(i) E ⟶ event of getting girl name
No. of favorable outcomes = 18 (18 girls)
Probability, P(E) = (No.of favorable outcomes)/(Total no.of possible outcomes) = 18/34 = 9/17
(ii) E ⟶ event of getting boy name
No. of favorable outcomes = 16 (16 boys)
P(E) = 16/34 = 8/17