(a) Compute the sums of the squares of Rows 1-4 of Pascal's Triangle. That is, compute:
1 answer:
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The answer is 067.
It takes an even number of steps for the object to reach (2,2), so the number of steps the object may have taken is either 4 or 6 .
If the object took 4 steps, then it must have gone two steps and two steps E, in some permutation. There are
ways for these four steps of occuring, and the probability is
.
If the object took 6 steps, then it must have gone two steps N and two steps E, and an additional pair of moves that would cancel out, either N / S or W/E. The sequences N, N, N, E, E, S can be permuted in ways. However, if the first four steps of the sequence are N, N, E, E in some permutation, it would have already reached the point (2,2) in four moves. There are
ways to order those four steps and
ways to determine the order of the remaining two steps, for a total of 12 sequences that we have to exclude. This gives
sequences of steps. There are the same number of sequences for the steps N, N, E, E, E, W, so the probability here is
.
The total probability is , and
.
What is probability?
- Probability is synonymous with possibility. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one.
- Probability has been introduced in mathematics to predict the likelihood of occurrences occurring. Probability is defined as the degree to which something is likely to occur.
- This is the fundamental probability theory, which is also utilized in probability distribution, in which you will learn about the possible results of a random experiment.
- To determine the likelihood of a particular event occurring, we must first determine the total number of alternative possibilities.
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