A constitutional amendment has the support of 65 out of 100 senators and 292 out of 435 members of the House of Representatives. In order to become law, the amendment must have a 2/3 super majority by both the House and the Senate and also have the support of 75% of the states. Forty states have voted their support. Is it possible for the amendment to become law? Explain.
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
A constitutional amendment has the support of 65 out of 100 senators and 292 out of 435 members of the House of Representatives. In order to become law, the amendment must have a 2/3 super majority by both the House and the Senate and also have the support of 75% of the states. Forty states have voted their support. Is it possible for the amendment to become law? Explain.
The objective here is to mathematically determine whether the amendment will become a law, based on the number of supports given.
There are two basic requirements:
1) The amendment must have super majority by both the House and the Senate.
2) The amendment must have the support of 75% of the states.
We shall check the eligibility one-by-one.
It is given that the amendment has the support of 65 out of 100 senators and 292 out of 435 members of the House of Representatives.
That is, a total of 357 supporters out of 535 people. This implies that 66.7290% of the people are in the favour of the bill, whereas the requirement is of . Clearly as, 66.7290 > 66.6667, we can say that it has qualified the first stage of voting.
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