Hospital records show that of patients suffering from a certain disease, 25% die of it. Compute and plot a bar graph of the probability distribution of recoveries out of 6 randomly selected patients
Let "X=" the number of recovered patients: "X\\sim Bin(n, p)."
Given "n=6, q=0.25, p=1-q=1-0.25=0.75."
"P(X=0)=\\dbinom{6}{0}(0.75)^0(0.25)^{6-0}""=0.0002"
"=0.0044"
"=0.0330"
"=0.1318"
"=0.2966"
"=0.3560"
"=0.1780"
The mode is an integer "M" that satisfies
"(6+1)\\cdot0.75-1\\leq M<(6+1)\\cdot0.75"
"4.25\\leq M<5.25"
"M=5"
"P(X=5)=\\dbinom{6}{5}(0.75)^5(0.25)^{6-5}"
"=0.35595703125"
The most probable number of recoveries out of 6 randomly selected patients is "5" patients.
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