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Answer the following.
Children of a society practise building human pyramids for 16 days to participate in the pyramid…
Children of a society practise building human pyramids for 16 days to participate in the pyramid building competition during the Janmashtami festival.
During practice sessions, the number of pyramids successfully formed in a day are $X = 0, 1, 2, 3, 4$. The data of the practice sessions is given in the following table:
| Pyramids made ($X$) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| No. of days | 1 | 4 | 6 | $x$ | 1 |
(a)[1.0]
Find the number of days on which the children made 3 pyramids.
(b)[2.0]
Form a probability distribution table for the number of pyramids made per day. Verify if it is a valid probability distribution table.
(c)[1.0]
Calculate the average number of pyramids formed.
Answer
Answer (b)
AIProbability distribution table:
Verification:
Each $P(X = x_i) \ge 0$ and $\sum P(X) = \frac{1 + 4 + 6 + 4 + 1}{16} = \frac{16}{16} = 1$.
Since all probabilities are non-negative and their sum is equal to 1, it is a valid probability distribution table.
| $X$ | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| $P(X)$ | $\frac{1}{16}$ | $\frac{4}{16}$ | $\frac{6}{16}$ | $\frac{4}{16}$ | $\frac{1}{16}$ |
From ISC 2026 Mathematics Paper 1, question 10(ii).
Check your working with the Probability distribution calculator: find k, the mean, variance and standard deviation of a random variable, with the working table.