The answer and explanation to question 1
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Using the hypergeometric distribution, it is found that there is a 0.4286 = 42.86% probability of getting 2 of the same colour.
The marbles are chosen without replacement, hence the <em>hypergeometric </em>distribution is used to solve this question.
<h3>What is the hypergeometric distribution formula?</h3>The formula is:
The parameters are:
- x is the number of successes.
- N is the size of the population.
- n is the size of the sample.
- k is the total number of desired outcomes.
In this problem:
- There is a total of 3 + 4 = 7 marbles, hence N = 7.
- Of those, 3 are blue, hence k = 3.
- 2 marbles will be taken, hence n = 2.
The probability of getting 2 of the same colour is the sum of P(X = 0), which is both red, with P(X = 2), which is both blue, then:
Hence:
0.4286 = 42.86% probability of getting 2 of the same colour.
You can learn more about the hypergeometric distribution at brainly.com/question/4818951
There are 12 such shapes. One can start with two squares, adding squares around the edge and rejecting shapes that have been previously seen. Repeating until you have 5 squares results in 12 distinct shapes.
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2 shapes are possible with 3 squares: L, I
5 shapes are possible with 4 squares: L, I, N, T, O
