A viral infection is spread by contact with an infectedperson. Suppose that a he

Question

A viral infection is spread by contact with an infectedperson. Suppose that a healthy person as a 40% chance ofcontracting the infection in one contact. An infected person hascontact with four healthy persons. Let X denote the number ofpeople that are not infected. Find the probability that at leastthree people are infected. Could you show all formulas and work, so I can trulyunderstand. Thank you. A viral infection is spread by contact with an infectedperson. Suppose that a healthy person as a 40% chance ofcontracting the infection in one contact. An infected person hascontact with four healthy persons. Let X denote the number ofpeople that are not infected. Find the probability that at leastthree people are infected. Could you show all formulas and work, so I can trulyunderstand. Thank you.

Explanation / Answer

n=4 because there are 4 healthy people in contact with theinfected person. x= number that are not infected P=.6 because you have a 40% of contracting the virus so youhave a 60% chance of not catching the virus. Use a binomial property because you can label success or failure,sick or not. And there is a set probability and number oftrials. So P(x=...)= n (nCr) x (p)^x (1-p)^(n-x) so in this you are looking for at least 3 infected so you need 0 or1 not infected. This gives us the P(x=0) + P(x=1) = the probability at least 3 areinfected. P(x=0) = 4 nCr 0 (.6)^0 (.4)^4 = .0256 P(x=1) = 4 nCr 1 (.6)^1 (.4)^3 = .1536 So P(x=0) + P(x=1) = .0256+.1536 = .1792 So the probability of at least 3 people getting infected in .1792.Also said as 17.92%. I hope this helps. Message me for more information.

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