A small college has 800 students, $10 \%$ of which are left-handed. Suppose they take an SRS of 8 students. Let $L=$ the number of left-handed students in the sample.

Which of the following would find $P(L=2)$ ?
Choose 1 answer:
(A) $\binom{800}{8}(0.10)^{2}(0.90)^{6}$
(B) $\binom{8}{2}(0.10)^{6}(0.90)^{2}$
(c) $\binom{8}{2}(0.10)^{2}(0.90)^{6}$
(D) $(0.10)^{6}(0.90)^{2}$
(E) $(0.10)^{2}(0.90)^{6}$

Question

A small college has 800 students, $10 \%$ of which are left-handed. Suppose they take an SRS of 8 students. Let $L=$ the number of left-handed students in the sample.

Which of the following would find $P(L=2)$ ?
Choose 1 answer:
(A) $\binom{800}{8}(0.10)^{2}(0.90)^{6}$
(B) $\binom{8}{2}(0.10)^{6}(0.90)^{2}$
(c) $\binom{8}{2}(0.10)^{2}(0.90)^{6}$
(D) $(0.10)^{6}(0.90)^{2}$
(E) $(0.10)^{2}(0.90)^{6}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the correct binomial probability formula for the given scenario: $P(L=k) = \binom{n}{k}p^k(1-p)^{n-k}$ where $n$ is the number of trials, $k$ is the number of successes, and $p$ is the probability of success. ‖ ‖ step 2 ⋮ Determine the values for $n$, $k$, and $p$: $n=8$ (sample size), $k=2$ (number of left-handed students), and $p=0.10$ (probability of being left-handed). ‖ ‖ step 3 ⋮ Apply the values to the binomial probability formula: $P(L=2) = \binom{8}{2}(0.10)^2(0.90)^{8-2}$. ‖ ***C*** ∻Key Concept∻ ⚹Binomial Probability Distribution⚹ ∻Explanation∻ ⚹The binomial probability distribution is used to calculate the probability of having a certain number of successes in a fixed number of independent trials, with a constant probability of success on each trial.⚹◊What is the formula for calculating the probability of having exactly 2 left-handed students in a sample of 8 students based on the scenario provided?⍭ Generate me a similar question◊

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