In a survey of 300 college graduates, 63% reported that they entered a profession closely related to their college major. If 9 of those survey subjects are randomly selected without replacement for a follow-up survey, what is the probability that 4 or fewer of them entered a profession closely related to their college major?
A)0.793

B)0.0512

C)0.149

D)0.207

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MathPhys MathPhys · Answer 1 · 2020-01-14T20:31:35+01:00

Answer:

D) 0.207

Step-by-step explanation:

Binomial probability:

P = nCr pʳ qⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1−p).

Here, n = 9, p = 0.63, and q = 0.37.

If r = 4:

P = ₉C₄ (0.63⁴) (0.37⁹⁻⁴)

P = 0.1376

If r = 3:

P = ₉C₃ (0.63³) (0.37⁹⁻³)

P = 0.0539

If r = 2:

P = ₉C₂ (0.63²) (0.37⁹⁻²)

P = 0.0136

If r = 1:

P = ₉C₁ (0.63¹) (0.37⁹⁻¹)

P = 0.0020

If r = 0:

P = ₉C₀ (0.63⁰) (0.37⁹⁻⁰)

P = 0.0001

The total probability is:

P = 0.1376 + 0.0539 + 0.0136 + 0.0020 + 0.0001

P = 0.2072