1. A student said that the probability of selecting a king from a standard deck
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Question
1. A student said that the probability of selecting a king from a standard deck of cards is 4/52 and the probability of selecting a heart is 13/52, so the probability of selecting a king or a heart must be 4/52 + 13/52 = 17/52.
Is this true? Explain why or why not.
2. A student is randomly selected from a group of 200 students in which 135 take math, 85 take English, and 65 take both math and English.
a) Find the probability that the selected student takes math or English.
b) Find the probability the selected student does not take math.
c) Find the probability the selected student takes neither math nor English.
Explanation / Answer
1)
P( A OR B) = P(A) + P(B) - P( A AND B)
Therefore,
P( King Or a heart) = P(King) + P(heart) - P( King of heart )
= 4/52 + 13/52 - 1/52
= 16/52
2)
a)
P( Math OR english) = P(Math) + P(English) - P( Math And English)
= (135 / 200) + (85 / 200) - (65 / 200)
= 155 / 200
= 0.775
Probability that selected student take Math or English = 0.775
b)
P( Mathc ) = P(English) - P( Math And English)
= 85 / 200 - 65 / 200
= 20/200
= 0.10
Probability that selected student does not take math = 0.10
c)
P(Neither Math nor english) = 1 - P( math OR English)
= 1 - 155/200
= 45/200
= 0.225
Probability that selected student takes neither math nor english = 0.225
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