Question

Mrs. Gomes found that 40% of students at her high school take chemistry. She randomly surveys 12 students. What is the probability that exactly 4 students have taken chemistry? Round the answer to the nearest thousandth. A)0.005 B)0.008 C)0.213 D)0.227

Answer 1

The correct option is C. 0.213

Explanation:

Percentage of students at high school who takes chemistry = 40%

So, probability of students who take chemistry = 0.4

So, probability of students who do not take chemistry = 1 - 0.4

= 0.6

Total number of students taken for survey = 12

Now, we need to find the probability that exactly 4 students have taken chemistry among the 12 surveyed students.

By using binomial distribution :

n = 12 , p = 0.4 , q = 0.6 , k = 4

`\text{Required Probability = }_(k)^(n)\textrm{C}\cdot(p)^k\cdot(q)^(n-k)\\\\\implies\text{Required Probability = }_(4)^(12)\textrm{C} \cdot(0.4)^4 \cdot(0.6)^8 \\\\\implies \text{Required Probability = }0.2128\approx 0.213`

Therefore, The correct option is C. 0.213

Answer 2

Binomial formula is :

`P ( k = 4 ) = nCk * p ^(k)(1-p) ^(n)= \\ =495 * 0.4 ^(4)* ( 0.6 ) ^(8)=`
= 495 * 0.0256 * 0.0167961 =
= 0.21284 ≈ 0.213
Answer: C ) 0.213