3. In testing a new drug, researchers found that 10% of all patients using it will have a mild side effect. A random sample of 14 patients using the drug is selected. Find the probability that:
(A) exactly two will have this mild side effect
(B) at least three will have this mild side effect.
I got this for (A):
= 14!/(14-2)!2! (0.10)²(0.90)14-2^2
= 14*13*12!/12!2*1(0.10)²(0.90)12^2
= 14*13/2*1(0.01)(0.28)
= 182/2(0.01)(0.28)
= 91(0.01)(0.28) = 0.25 or 25%
But i'm not sure how to do (B)
PLZZZZZ HELP!!!
A looks OK!
For B, use the same process. Since the problem says "at least 3" you will have to determine P(0), P(1), P(2). You already have P(2) from part A. Add P(0), P(1), and P(2) together. Then subtract that value from 1 for your probability.
I hope this helps.
SPAMA GUY!!! LOLOLATRA HAIL BIN LADIN!
To calculate the probability that at least three patients will have the mild side effect, you'll need to consider all the possible scenarios where three or more patients experience the side effect.
To simplify the calculation, you can calculate the probability of the complementary event, which is the probability that two or fewer patients will have the side effect. Then, subtracting this probability from 1 will give you the desired probability.
To find the probability of two or fewer patients experiencing the side effect, you need to calculate the probabilities for each case separately and then add them together.
Let's break it down:
1. Probability of exactly zero patients having the side effect:
P(X = 0) = (0.10)^0 * (0.90)^14 = (1) * (0.90)^14
2. Probability of exactly one patient having the side effect:
P(X = 1) = C(14, 1) * (0.10)^1 * (0.90)^13
3. Probability of exactly two patients having the side effect:
P(X = 2) = C(14, 2) * (0.10)^2 * (0.90)^12
To get the value of C(n, r) (combination) where n is the total number of trials and r is the number of successful trials, you can use the formula:
C(n, r) = n! / (r!(n-r)!)
Note: In this case, n = 14.
Now that you have calculated these three probabilities, you can add them together:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
Finally, to find the probability of at least three patients having the mild side effect, subtract the result from 1:
P(X ≥ 3) = 1 - P(X ≤ 2)
By plugging the values into these equations and performing the calculations, you'll find the probability for part (B).