A class contains 15 male and 10 female students. If half of the male and half of

Question

A class contains 15 male and 10 female students. If half of the male and half of the female are taller than 6 feet, what is the probability that a student selected at random is a male or is taller than 6'. Based on a survey amongst 120 students, 60 are studying French, 50 are studying Spanish, and 20 are studying both. If a student is chosen at random what is the probability that student is studying: a) French or Spanish, b) Neither French nor English, c) Exactly one of the two languages. Show the proof that P(A^c) = 1 - P(A) A game consists of tossing a fair coin four times. A player wins $3 if two or more heads appear, otherwise the player will lose $2. Determine if this game is fair or not to the player on the average.

Explanation / Answer

1)let male be represnted as m and taller than 6 ft as t then P(m or t )=P(m)+P(t)-P(m and t)

P(m or t) =15/25+12.5/25+7.5/25 = 35 /25 = 7/5

2)a)P(F or S)= P(F)+P(S)-P(F and S)

=60/120+50/120-20/120 = 90/120 = 3/4

b)if a draw aven diagram then , enter 20 in the intersection region and 40 in the non overlapping part of french and 30 in the non overlapping part spanish . Number that dont knw niether french nor spanish = 120- (20+40+30) = 30

so its probability is 30/120 = 1/4

c)those who knwo exactly one language is 40+30 = 70

so its probability = 70/120 = 7/12

3)A union A' = S

Probability on both side = P(A U A') = P(S)

P(A)+P(A')= P(S)(they are disjoints)

ie P(A) +P(A') = 1 since P(s) = n(s) /n(s) =1

so P(A')= 1 -P(A)

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