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A new drug on the market is known to cure 24% of patients with colon cancer. If a group of 15 patients is randomly selected, what is the probability of observing, at most, two patients who will be cured of colon cancer?

A. 15 choose 2(0.24)2(0.76)13
B. 15 choose 0(0.76)15 + 15 choose 1(0.24)1(0.76)14 + 15 choose 2(0.24)2(0.76)13
C. 1 − 15 choose 2(0.24)2(0.76)13
D. 15 choose 0 (0.76)15
E. 1 − 15 choose 0 (0.76)15

Respuesta :

MrRoyal

The expression for the probability that at most 2 of the 15 samples are cured is:

[tex]P(x \le 2) = ^{15}C_0 (0.24)^0(0.76)^{15} + ^{15}C_1 (0.24)^1(0.76)^{14} + ^{15}C_2 (0.24)^2(0.76)^{13}[/tex]

Probabilities

Probabilities are used to determine the chances of events.

The given parameters are:

  • [tex]n = 15[/tex] -- the sample size
  • [tex]p = 24\%[/tex] --- the proportion of patients the drug can cure

The probability that at most 2 of the 15 samples are cured is represented as:

[tex]P(x \le 2)[/tex]

Binomial probability

This is calculated using the following binomial probability formula

[tex]P(X \le x) = ^nC_x p^x(1 - p)^{n-x}[/tex]

So, we have:

[tex]P(x \le 2) = ^{15}C_0 (0.24)^0(1 - 0.24)^{15} + ^{15}C_1 (0.24)^1(1 - 0.24)^{14} + ^{15}C_2 (0.24)^2(1 - 0.24)^{13}[/tex]

Simplify

[tex]P(x \le 2) = ^{15}C_0 (0.24)^0(0.76)^{15} + ^{15}C_1 (0.24)^1(0.76)^{14} + ^{15}C_2 (0.24)^2(0.76)^{13}[/tex]

Hence, the expression for the probability is:

[tex]P(x \le 2) = ^{15}C_0 (0.24)^0(0.76)^{15} + ^{15}C_1 (0.24)^1(0.76)^{14} + ^{15}C_2 (0.24)^2(0.76)^{13}[/tex]

Read more about probabilities at:

https://brainly.com/question/15246027

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