In a quarter pound bag of red pistacio nuts, some shells are to difficult to pry

Question

In a quarter pound bag of red pistacio nuts, some shells are to difficult to pry open by hand. Suppose the random variable X, the number of pistachios in a randomly selected bag that cannot be opened by hand, has the probability distrubution given in the table below.

x 0 1 2 3 4 5

p(x) .5 .25 .1 .05. .075 .025

a.) Find the probability X takes on a value less than the mean

b.) Suppose two bags of pistachios are selected at random. What is the probability that both bags have four or more pistachios too dificult to open by hand?

Explanation / Answer

mean = 0*0.5+1*0.25+2*0.1+3*0.05+4*0.075+5*0.025 = 1.025

values less than mean are 0,1

probability X takes on a value less than the mean = P(0) +P(1) = 0.5+0.25 = 0.75

b)Probablity that bag contains four or more pistachios too dificult to open by hand = P(4)+P(5) = 0.075+0.025 = 0.1

probability that both bags have four or more pistachios too dificult to open by hand = 0.1*0.1 = 0.01

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.