Let p=0.11 and q=0.62. What is P[X=0|Y=0]?

Question

BlackTom AI · Accepted Answer

The question states: Let p = 0.11 and q = 0.62. What is P[X=0 | Y=0]? There is no information about how X and Y are related.

First, recognize what P[X=0 | Y=0] means: the probability that X equals 0 given that Y equals 0. By definition, this conditional probability depends on the joint distribution of (X, Y).

If X and Y are independent Bernoulli random variables with P(X=1) = p and P(Y=1) = q, then P(X=0 | Y=0) equals P(X=0), because Y gives no information about X under independence. In that case:
- P(X=0) = 1 - p = 1 - 0.11 = 0.89.
- Therefore P[X=0 | Y=0] = 0.89.

If, on the other hand, X and Y are not independent, you cannot determine P[X=0 | Y=0] from p and q alone. You would need the joint distribution, specifically P(X=0, Y=0) and P(Y=0), because:
- P[X=0 | Y=0] = P(X=0, Y=0) / P(Y=0).
- If you know P(X=0, Y=0) and P(Y=0) from a given joint model, you could compute the ratio directly.

Alternatively, if you know P(X=1, Y=0) or P(X=0, Y=1), you could derive P(X=0, Y=0) using the fact that the margins are constrained by p and q, but still you would need enough information to fix the joint structure.

Given the data provided (p = 0.11, q = 0.62) and no joint information, the value 0.2386 cannot be derived from these numbers alone. If the problem intended independence, the result would be 0.89; if not, one must know P(X=0, Y=0) or the dependency to compute P[X=0 | Y=0].

In summary:
- Under independence: P[X=0 | Y=0] = 1 - p = 0.89.
- Under dependence: need P(X=0, Y=0) and P(Y=0) to compute the conditional probability; the given 0.2386 cannot be justified without that joint information.

If you can provide the joint distribution or specify whether X and Y are independent, I can compute the exact P[X=0 | Y=0].

COMM_V 190 101-104 2025W1 2025W1 COMM 190 Final Exam - TUE Dec 09 2025 - Requires Respondus LockDown Browser

Let p=0.11 and q=0.62. What is P[X=0|Y=0]?

查看解析

登录即可查看完整答案

类似问题

Based on this contingency table the probability that a person who tested positive for asthma has asthma is

What is the probability that an athlete is not a drug user, given that the test is negative?

位置11的问题 The probability that a student gets a score above 70 on this exam given that they studied is necessarily equal to the probability that a student studied given that they got above a 70 on this exam.TrueFalseDon't Know清除选择

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单