Probabilidade Exercicios Resolvidos «2026 Update»

Favorable pairs: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) → 6 outcomes. [ P(\textsum = 7) = \frac636 = \frac16 \approx 0.1667 ]

Given: [ P(D) = 0.001,\quad P(T^+|D) = 0.99,\quad P(T^+|\neg D) = 0.01 ] By Bayes' theorem: [ P(D|T^+) = \fracD)P(D)D)P(D) + P(T^+ ] [ = \frac0.99 \times 0.0010.99 \times 0.001 + 0.01 \times 0.999 ] [ = \frac0.000990.00099 + 0.00999 = \frac0.000990.01098 \approx 0.09016 ] probabilidade exercicios resolvidos

( \frac516 ). Exercise 6: Complement and "At Least One" Problem: If you roll a fair die 3 times, what is the probability of getting at least one 6? Solution: Easier to use complement: [ P(\textat least one 6) = 1 - P(\textno 6) ] Probability of no 6 in one roll = ( \frac56 ). [ P(\textno 6 in 3 rolls) = \left(\frac56\right)^3 = \frac125216 ] [ P(\textat least one 6) = 1 - \frac125216 = \frac91216 \approx 0.4213 ] Favorable pairs: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)

About 9.02%. Despite high accuracy, low prevalence means most positives are false positives. Exercise 5: Binomial Probability Problem: A fair coin is tossed 5 times. What is the probability of getting exactly 3 heads? Solution: Binomial with ( n=5, k=3, p=0.5 ): [ P(X=3) = \binom53 (0.5)^3 (0.5)^2 = 10 \times (0.5)^5 ] [ = 10 \times \frac132 = \frac1032 = \frac516 = 0.3125 ] Solution: Easier to use complement: [ P(\textat least