A teacher decides to award exam grades A,B or C by a new method. Out of 20 children,three are to receive A's, five are to receive B's and the rest C's. She wrote the letters A,B and C on 20 pieces of paper and invite the student to draw their exam result, going through the classes in alphabetical order. Find the probability that:
a) The first three students all get grade 'A'
b) The first three students all get grade 'B'
c) The first three students all get different grades.
d) The first four students all get grade'B'
( Do not cancle down the fractions)
Answers
Answer:
There are 3 A's, 5 B's and 12 C's
a)Probability that first gets A = 3/20
When first has got A, then there are 19 pieces of paper in which there are 2 A's
Therefore, probability that second gets A = 2/19
When second also has got A, then there are 18 pieces of paper in which there is 1 A.
Therefore probability that third gets A = 1/18
Therefore probability that first three get A's
= 3/20 * 2/19 * 1/18
= 1/1140
b)Probability that first gets A = 5/20 = 1/4
When first has got B, then there are 19 pieces of paper in which there are 4 B's
Therefore, probability that second gets B = 4/19
When second also has got B, then there are 18 pieces of paper in which there are 3 B's.
Therefore probability that third gets B = 3/18 = 1/6
Therefore probability that first three get B's
= 1/4 * 4/19 * 1/6
= 1/114
c)Probability that first gets A = 3/20
Probability that second gets B = 5/19
Probability that third gets C = 12/18 = 2/3
Combined probability of above three events = 3/20 * 5/19 * 2/3
= 1/38
If their grades are shuffled among themselves, then also they will have different grades. The grades of first three can be shuffled in 3! = 6 ways.
Therefore probability that first three get different grades = 1/38 * 6 = 3/19
d) In (b), we calculated that the probability first three get B = 1/114
When first three have got B, then there are 17 pieces of paper in which there are 2 B's.
Therefore probability that fourth gets B = 2/17
Therefore probability that first four get B
= 1/114 * 2/17
= 1/969
Step-by-step explanation:
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