Question

ERROR ANALYSIS In Exercises 15 and 16, describe and correct the error in calculating the probability of rolling a 1 exactly 3 times in 5 rolls of a six-sided die. 15. X $P(k = 3) = \binom{5}{3} \left(\frac{1}{6}\right)^{5 - 3} \left(\frac{5}{6}\right)^3$ $\approx 0.161$ 16. X $P(k = 3) = \left(\frac{1}{6}\right)^3 \left(\frac{5}{6}\right)^{5 - 3}$ $\approx 0.003$

          ERROR ANALYSIS In Exercises 15 and 16, describe and
correct the error in calculating the probability of rolling
a 1 exactly 3 times in 5 rolls of a six-sided die.
15.
X \(P(k = 3) = \binom{5}{3} \left(\frac{1}{6}\right)^{5 - 3} \left(\frac{5}{6}\right)^3\)
\(\approx 0.161\)
16.
X \(P(k = 3) = \left(\frac{1}{6}\right)^3 \left(\frac{5}{6}\right)^{5 - 3}\)
\(\approx 0.003\)

ERROR ANALYSIS In Exercises 15 and 16, describe and
correct the error in calculating the probability of rolling
a 1 exactly 3 times in 5 rolls of a six-sided die.
15.
X P(k = 3) = 53((1)/(6))^5 - 3((5)/(6))^3
≈ 0.161
16.
X P(k = 3) = ((1)/(6))^3 ((5)/(6))^5 - 3
≈ 0.003

Added by Catalina C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Diwakar Mandilwar

Step 1

We have n = 5 independent rolls, success = rolling a 1 with p = 1/6, and k = 3 successes. Use the binomial formula: P(X = k) = C(n,k) p^k (1 - p)^(n - k). So the correct expression is P(X = 3) = C(5,3) (1/6)^3 (5/6)^2. Show more…

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ERROR ANALYSIS In Exercises 15 and 16, describe and correct the error in calculating the probability of rolling a 1 exactly 3 times in 5 rolls of a six-sided die. 15. XP(k = 3) = $_5C_3 (\frac{1}{6})^{5-3} (\frac{5}{6})^3$ ≈ 0.161 16. XP(k = 3) = $(\frac{1}{6})^3 (\frac{5}{6})^{5-3}$ ≈ 0.003