Question

BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game. The table given below, shows the data of one such game where 48 balls were used before Tara said 'BINGO'. Number announced Number of times 0 - 15 8 15 - 30 9 30 - 45 10 45 - 60 12 60 - 75 9

Based on the above information, answer the following:

1. Write the median class.   [1]
2. When first ball was picked up, what was the probability of calling out an even number?   [1]
3.   
   1. Find median of the given data.   [2]
                          OR
   2. Find mode of the given data.   [2]

Answer 1

i. 

Number Announced	Number of times	c.f.
0 - 15	8	8
15 - 30	9	17
30 - 45	10	27
45 - 60	12	39
60 - 75	9	48
	N = 48

Here, N = 48

then `N/2 = 48/2 = 24`

∴ Median class: 30 − 45

ii. The number of even numbers between 1 to 75 is 37, [i.e., (75 − 1) ÷ 2 = 37)

Prob.(calling out an even number) = `37/75`

iii.

a. From part (i), we have median class: 30 − 45

We have, l = 30, c.f. = 17, f = 10, h = 15

Median = `l + (N/2 - c.f.)/(f) xx h`

= `30 + (24 - 17)/(10) xx 15`

= `30 + 7/10 xx 15`

= `30 + 105/10`

= 30 + 10.5 

= 40.5

                                                     OR

b. From part (i), we see the highest frequency is 12. So, the modal class is 45 − 60.

l = 45, f₀ = 10, f₁ = 12, f₂ = 9, h = 15

Mode = `l + ((f_1 - f_0)/(2f_1 - f_0 - f_2)) xx h`

= `45 + ((12 - 10)/(2 xx 12 - 10 - 9)) xx 15`

= `45 + (2/(24 - 19)) xx 15`

= `45 + 2/5 xx 15`

= 45 + 6

= 51