Answer:
Step-by-step explanation:
1 ) No of total slips after addition = 11
8 slip with 3 on it
3 slips with 9 on it
expectation value = probability of 3 x 3 + probability of 9 x 9
= (8 / 11) x 3 + (3 / 11) x 9
24 / 11 + 27 / 11 = 4.636
2 )
No of total slips after addition = 12
8 slip with 3 on it
4 slips with 9 on it
expectation value = probability of 3 x 3 + probability of 9 x 9
= (8 / 12) x 3 + (4 / 12) x 9
2 + 3 = 5
3 )
Let n be the required number
No of total slips after addition = 10+n
8 slip with 3 on it
2 + n slips with 9 on it
expectation value = probability of 3 x 3 + probability of 9 x 9
= (8 / 10+n ) x 3 + (2+n / 10+n ) x 9 = 6
24 + 18 + 9n / 10 + n = 6
42 + 9n = 60 + 6n
3 n = 18
n = 6
4 )
Let n be the required number
No of total slips after addition = 10+n
8 slip with 3 on it
2 + n slips with 9 on it
expectation value = probability of 3 x 3 + probability of 9 x 9
= (8 / 10+n ) x 3 + (2+n / 10+n ) x 9 = 8
24 + 18 + 9n / 10 + n = 8
42 + 9n = 80 + 8n
n =
n = 38
Minimum of 38 has to be added .
