Find an $x$ such that mutually exclusive events are to disjoint sets what independent events are to $x$

Paxton Hoffman
2022-07-20
Answered

Find an $x$ such that mutually exclusive events are to disjoint sets what independent events are to $x$

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Brendon Bentley

Answered 2022-07-21
Author has **11** answers

In pure set theoretic terms, there is no notion of measure, so it is difficult to talk about events being independent. Disjoint events are those with no overlap, and you don't need a notion of measure to say that two sets have no elements in common.

To capture the notion of independence, we would have to say that the proportion of set $A$ that overlaps with set $B$ is the same as the proportion of the universal set that set $B$ occupies. In pure set theory, there's not really any need for talking about sets in this way, unless we're doing probability.

To capture the notion of independence, we would have to say that the proportion of set $A$ that overlaps with set $B$ is the same as the proportion of the universal set that set $B$ occupies. In pure set theory, there's not really any need for talking about sets in this way, unless we're doing probability.

asked 2021-11-07

Jenny sells ‘honey tea’ to raise fund for homeless people. The probability of making a sale is, independently, 0.3 for each person she approaches

Based on Jenny’s experience selling ‘honey tea’ for the last 2 weeks, the probability that the person she approaches will buy 0, 1, 2 or more than 2 cups are 0.7, 0.15, 0.10 and 0.05 respectively. Jenny plans to approached 20 persons. What is the probability that 10 will not buy, 3 will buy 1 cup, 4 will buy 2 cups and the rest will buy than 2 cups?

Based on Jenny’s experience selling ‘honey tea’ for the last 2 weeks, the probability that the person she approaches will buy 0, 1, 2 or more than 2 cups are 0.7, 0.15, 0.10 and 0.05 respectively. Jenny plans to approached 20 persons. What is the probability that 10 will not buy, 3 will buy 1 cup, 4 will buy 2 cups and the rest will buy than 2 cups?

asked 2021-12-14

Consider a share that is modelled by a binomial random variable. The probability that the share increases in value by 20¢ in one month is 0.6. The probability that it decreases in value by 20¢ in one month is 0.4. The share is held for 5 months then sold. Let X denote the number of increases in the price of the share over the 5 months. В (п,

(a) What is n and p if$X\sim B(n,p)?$

(b) Find$E\left(X\right){\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\sigma \left(X\right)$ .

(c) Let Y be the random variable which models the change in share price. Then$\u04ae-0.2X-0.2(n-X)$ because 0.2X is the total increase in share price and $0.2(n-X)$ is the total decrease in share price. Simplify the expression for Y in terms of X. Then using (b), find E(Y) and $\sigma \left(Y\right)$ .

(a) What is n and p if

(b) Find

(c) Let Y be the random variable which models the change in share price. Then

asked 2021-12-17

Beth is taking an eleven-question multiple-choice test for which each question has three answer choices, only one of which is correct. Beth decides on answers by rolling a fair die and marking the first answer choice if the die shows 1 or 2, the second if the die shows 3 or 4, and the third if the die shows 5 or 6. Find the probability of the stated event.

exactly

four

correct answers

exactly

four

correct answers

asked 2022-02-14

If $P\left(A\right)=0.8,P\left(B\right)=0.9,\text{and}\text{}P(A\cap B)=0.8$ , what is $P\left(B\mid A\right)$ ? What about $P\left(A\mid B\right)$ ?

asked 2022-02-13

A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly three sixes?

asked 2021-09-17

The Metropolis police station calls Superman an average of 3 times per hour
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dependent only on the length of the time interval and, furthermore, is independent of whether
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If the number of times he is called is independent from one hour to the next, what is the probability that Superman and Lois can finish their 4 hour date uninterrupted?

If the number of times he is called is independent from one hour to the next, what is the probability that Superman and Lois can finish their 4 hour date uninterrupted?

asked 2021-09-28

Can be given binomail probability approximated by the normal probability destribution? p=.20 and n=100