Question

In a class of 35 students are numbered from 1 to 35 the ratio of boys to girls is 4:3 the roll numbers of students begin with boys and end with girls find the probability that a student selected is either a boy with Prime roll number for a girl with composite roll number or an even roll number

Answer 1

4/7 is probability that a student selected is either a boy with Prime roll number or a girl with composite roll number or an even roll number

Step-by-step explanation:

35 students are numbered from 1 to 35

ratio of boys to girls is 4:3

=> Boys = (4/7)35 = 20

   Girls = (3/7)35 = 15

roll numbers of students begin with boys and end with girls

Boys roll number = 1 , 2 , 3..............................................., 19 , 20

Girls roll number = 21 , 22 , .............................................., 34 , 35

Boys with Prime roll number = 8

2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 ,  

Girls With Composite roll number or even roll number = 12

21 , 22 , 24 , 25 , 26 , 27 , 28 , 30 , 32 , 33 , 34 , 35

8 + 12 = 20

probability that a student selected is either a boy with Prime roll number or a girl with composite roll number or an even roll number

= 20/35

= 4/7

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Answer 2

Answer:

Step-by-step explanation:

35 students are numbered from 1 to 35

ratio of boys to girls is 4:3

=> Boys = (4/7)35 = 20

   Girls = (3/7)35 = 15

roll numbers of students begin with boys and end with girls

Boys roll number = 1 , 2 , 3..............................................., 19 , 20

Girls roll number = 21 , 22 , .............................................., 34 , 35

n(S) = 35

Let 'A' be an event of getting a boy with prime roll number = (2 , 3 , 5 , 7 , 11 , 13 , 17 , 19)

n(A) = 8

P(A) = 8/35

Let 'B' be an event of getting a girl with composite roll number = (21 , 22 , 24 , 25 , 26 , 27 , 28 , 30 , 32 , 33 , 34 , 35)

n(B) = 12

P(B) = 12/35

Let 'C' be an event of getting an even roll number = (2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 , 26 , 28 , 30 , 32 , 34)

n(C) = 17

P(C) = 17/35

A⋂B = ∅

P(A⋂B) = 0

B⋂C = (22 , 24 , 26 , 28 , 30 , 32 , 34)

n(B⋂C) = 7

P(B⋂C) = 7/35

C⋂A = (2)

n(C⋂A) = 1

P(C⋂A) = 1/35

A⋂B⋂C = ∅

P(A⋂B⋂C) = 0

Probability that a student selected is either a boy with prime roll number or a girl with composite roll number or an even roll number,

P(A⋃B⋃C) = P(A) + P(B) + P(C) - P(A⋂B) - P(B⋂C) - P(C⋂A) + P(A⋂B⋂C)

= 8/35 + 12/35 + 17/35 - 0 - 7/35 - 1/35 + 0

= (37-8)/35

= 29/35