Answer both parts of number 1 and number 2, please. (1). At a raffle, 1000 ticke

Question

Answer both parts of number 1 and number 2, please.

(1). At a raffle, 1000 tickets are sold at $2 each for four prices $500, $250, $150 and $75 Suppose you buy one ticket. Assuming the random variable X represents the value of your gain (Amount won cost of the ticket): Construct the probability mass function for the random variable X in tabular form. (2). Findings of a research states that the probability of an individual who is left-handed is 0.20. Consider a class of 20 students. (a). What is the probability that exactly 5 students in the class are left-handed? (b). What is the probability that at most 3 students in the class are left-handed?

Explanation / Answer

No of tickets = 1000

price of each ticket = $2

probabilty of getting no prize = 996/1000

probabilty of getting $500 = 1/1000

probabilty of getting $250 = 1/1000

probabilty of getting $150 = 1/1000

probabilty of getting $75 = 1/1000

(2)

Probabilty that individual is left handed = 0.20

no of students = 20

a)

probability that exactly 5 students in class are left-handed = (20C5)(0.20)5(1-0.20)15 = 0.1746

b)

probability that at most 3 students in class are left-handed

= P(0) +P(1) +P(2) +P(3)

= (20C0)(0.20)0(1-0.20)20 +(20C1)(0.20)1(1-0.20)19 + (20C2)(0.20)2(1-0.20)18 + (20C3)(0.20)3(1-0.20)17

= 0.4114

X P(X= x) $0-$2 = -$2 996/1000 $500-$2 = $498 1/1000 $250-$2 = $248 1/1000 $150-$2 = $148 1/1000 $75-$2 = $73 1/1000

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