AI tutor | The No.1 Homework Finishing Free App
Statistics and Probability
Fundamentals of Probability - Sum of Probabilities (Addition Rule)
Q.01
'Explain the probability addition theorem using permutation methods.'
A. ...
Ask AI tutor for answer!
Join our DiscordQ.03
'In general, the following addition rule holds.\nAddition Rule\nLet two events A and B not occur simultaneously. If there are a ways for A to occur and b ways for B to occur, then\nThe total number of ways A or B can occur is a + b\nThe addition rule also holds for three or more events.'
A. ...
Ask AI tutor for answer!
Join our DiscordQ.04
'Provide the formula that satisfies the following relationship.'
A. ...
Ask AI tutor for answer!
Join our DiscordQ.05
'In region A, measurements of the heights of 400 15-year-old boys were taken, with an average of 168.4 cm and a standard deviation of 5.7 cm. Determine the 95% confidence interval for the average height m cm of 15-year-old boys in region A.'
A. ...
Ask AI tutor for answer!
Join our DiscordQ.06
'Topic: Sum and product of random variables, binomial distribution'
A. ...
Ask AI tutor for answer!
Join our DiscordQ.08
'The complement of event A, \ar{A}, is the event where neither card is a heart, so P(A)=1-P(\ar{A})=1-\\frac{_{39} \\mathrm{C}_{2}}{_{52} \\mathrm{C}_{2}}=1-\\frac{19}{34}=\\frac{15}{34}. For event B, there are _{4} \\mathrm{C}_{2} ways to select two different suits, and each suit has 13 possible cards, so P(B)=\\frac{_{4} \\mathrm{C}_{2} \\times 13^{2}}{_{52} \\mathrm{C}_{2}}=\\frac{6 \\cdot 13^{2}}{26 \\cdot 51}=\\frac{26}{34}(=\\frac{13}{17}). Furthermore, event A \\cap B is when one card is a heart and the other card is a non-heart suit, so P(A \\cap B)=\\frac{_{13} \\mathrm{C}_{1} \\times_{39} \\mathrm{C}_{1}}{_{52} \\mathrm{C}_{2}}=\\frac{13 \\cdot 39}{26 \\cdot 51}=\\frac{13}{34}. Therefore, the required probability is P(A \\cup B)=P(A)+P(B)-P(A \\cap B)=\\frac{15}{34}+\\frac{26}{34}-\\frac{13}{34}=\\frac{14}{17}.'
A. ...
Ask AI tutor for answer!
Join our DiscordQ.09
'Please explain with an example how the law of addition holds.'