Question

You are bidding on four items available on an online shopping site. You think that for each bid you have a 35​% chance of winning​ it, and the outcomes of the four bids are independent events. Let X denote the number of winning bids out of the four items you bid on. Find the probabilities.

a. Find the probability that you win exactly 2 bids.

b. Find the probability that you win 2 bids or fewer.

c. Find the probability that you win more than 2 bids

Answer 1

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This is an application of binomial dist with params :

p = .35, n = 4 - B(n,p) = B(4, .35)

a.
P(X=2) = nCx*p^x *(1-p)^(n-x)
= 4C2 * (.35^2)*(.65^2)
= 0.3105

b. P(X<=2) =
=4C2 * (.35^2)*(.65^2)+4C1* (.35^1)*(.65^3)+4C0 * (.35^0)*(.65^4)
= 0.17850625 + 0.384475 + 0.3105375
= 0.8735

c. P(X>2) =
= 1- P(X<=2)
= 1-0.8735 ( we calculated P(X<=2) in part b above)
= 0.1265