Mathematics: Find the probability of at least three successes in six trials of a binomial experiment in which the probability of success is 50%. round to the nearest tenth of a percent.

Find the probability of at least three successes

Ответ:

mendezmarco2004

10.03.2022

Mathematics

$\dfrac{21}{32}=0.65625$

Step-by-step explanation:

If the probability of success is 50%, then p=0.5 and q=1-0.5=0.5.

At least three successes in six trials of a binomial experiment means that favorable are 3 successes, 4 successes, 5 successes and 6 successes.

1. 3 successes:

$Pr_1=C^3_6p^3q^{6-3}=\dfrac{6!}{3!(6-3)!}\cdot (0.5)^3\cdot (0.5)^3=20\cdot \dfrac{1}{2^6}=\dfrac{5}{16}$

2. 4 successes:

$Pr_2=C^4_6p^4q^{6-4}=\dfrac{6!}{4!(6-4)!}\cdot (0.5)^4\cdot (0.5)^2=15\cdot \dfrac{1}{2^6}=\dfrac{15}{64}$

3. 5 successes:

$Pr_3=C^5_6p^5q^{6-5}=\dfrac{6!}{5!(6-5)!}\cdot (0.5)^5\cdot (0.5)^1=6\cdot \dfrac{1}{2^6}=\dfrac{3}{32}$

4. 6 successes:

$Pr_4=C^6_6p^6q^{6-6}=\dfrac{6!}{6!(6-6)!}\cdot (0.5)^6\cdot (0.5)^1=1\cdot \dfrac{1}{2^6}=\dfrac{1}{64}$

Now, the probability of at least three successes in six trials of a binomial experiment is

$Pr=Pr_1+Pr_2+Pr_3+Pr_4=\dfrac{5}{16}+\dfrac{15}{64}+\dfrac{3}{32}+\dfrac{1}{64}=\dfrac{20+15+6+1}{64}=\dfrac{42}{64}=\dfrac{21}{32}=0.65625$

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Ответ:

angelequej1167

03.03.2020

Mathematics

John

Step-by-step explanation:

Quincy = Cinnamon

Lucy = Pumpkin

Prudence = Nutmeg

John = GINGER

Since Quincy used the most, that means he'd have the least remaining ingrediant (cinnamon - 1/4 || .25). If Lucy used the least of her ingrediant, then that means she'd have the most remaining, which would be the pumpkin (5/8 || .625). And if Prudence used more of his ingredient than John, that means she'd have less ingrediant remaining, so between the nutmeg and the ginger, she clearly used the nutmeg (1/3 || .33). Which leaves John with the Ginger (1/2 || .5)

(I know this is one of those free diamond grab questions, so I already confirmed the answer when I got 100%)

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Find the probability of at least three successes in six trials of a binomial experiment in which the probability of success is 50%. round to the nearest tenth of a percent.

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