Question

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

1. Find the number of days on which the children made 3 pyramids.
2. Form a probability distribution table for the number of pyramids made per day. Verify if it is a valid probability distribution table.
3. Calculate the average number of pyramids formed.

Answer 1

a. The total number of days of practice is given as 16. From the table, the sum of the number of days must equal 16.

1 + 4 + 6 + x + 1 = 16

12 + x = 16

x = 16 − 12

x = 4

So, there were 4 days on which the children made 3 pyramids.

b. To find the probability, we divide the number of days for each by the total number of days (16).

Pyramids made (X)	0	1	2	3	4
Probability P(X)	`1/16`	`4/16`	`6/16`	`4/16`	`1/16`

A probability distribution table is valid if the sum of all probabilities equals 1 (∑ P(X) = 1)

∑ P(X) = `1/16 + 4/16 + 6/16 + 4/16 + 1/16 = 16/16 = 1`

Since the sum is 1, it is a valid probability distribution table.

c. The average (Mean) is calculated using the formula:

µ = ∑[x.P(x)]

µ = `(0 × 1/16) + (1 × 4/16) + (2 × 6/16) + (3 × 4/16) + (4 × 1/16)`

µ = `0 + 4 + 12 + 12 + 4/16`

µ = `32/16`

µ = 2