A survey of high school juniors found that 82% of students plan on attending college. If you pick three at random, what is the probability that at least two plan on attending college? Round to the nearest percent.
I answered the question incorrectly, thinking it was 36% but the correct answer was 91%. Can someone please tell me what I did wrong and what is the rule or process I need to take. The book never showed me any other way to solve this just this: P(x) = nCx P^x q^n-x, I just want to learn the right way to avoid mistakes again for the upcoming test.
Please and thank you

91%

You forgot to add 'all three'

Step-by-step explanation:

X ~ B(3, 0.82)

q = 1 - 0.82 = 0.18

Atleast 2 means:

X = 2, or 3

3C2(0.82)²(0.18) + 3C3(0.82)³(0.18)⁰

= 0.363096 + 0.551368

= 0.914464

= 91.4464%

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

is there a picture

step-by-step explanation: