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Question
Two thirds of students in a class are boys and rest girls. It is known that the probability of a girl getting a first grade is 0.85 and that of boys is 0.70. Find the probability that a student chosen at random will get first grade marks.
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Solution
Let G be the event of choosing a boy and G be the event of choosing a girl.
Given P(B) = `2/3`
P(G) = `1/3`
Let B1 be the event of a boy getting first grade
P(B1) = 0.70
Let G1 be the event of a girl getting first grade
P(G1) = 0.85
Probability of a student getting a first grade = Probability of a boy getting first grade or Probability
of a Girl getting first grade
= P(B) × P(B1) + P(G) × P(G1)
= `2/3 xx 0.70 + 1/3 x 0.85`
= `(1.4 + 0.85)/3`
= `2.25/3`
= 0.75
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