Q. 5. A jar contains 6 red balls, 4 green balls,
3 blue balls, and 2 white balls. A sample of size
6 balls is selected at random without replacement.
Find the probability that the sample contains 2 red
balls, 2 green balls, 1 blue ball, and 1 white ball.
(June 2001)
Solution. Total number of balls = 6 + 4 +
3 + 2 = 15
Favourable cases = 6C2 X 4C2
X 3C1 X 2C1
A sample of size 6 balls is selected at random without
replacement.
Therefore, total number of cases = 15C6
| |
6C2 X 4C2
X 3C1 X 2C1
|
| Required probability = |
|
| |
15C6
|
| |
{(6!)/[(2!)(4!)]} X {(4!)/[(2!)(2!)]}
X {(3!)/[(1!)(2!)]} X {(2!)/[(1!)(1!)]}
|
| or Probability = |
|
| |
{(15!)/[(6!)(9!)]}
|
or Probability = 0.107
Q. 6. What is the probability that a leap year
selected at random contains 53 Sundays? (Dec.
98)
Solution. A leap year consists of 366 days
and, therefore, contains 52 complete weeks and 2 days
extra. These 2 days may make the following 7 combinations:
1. Monday and Tuesday
2. Tuesday and Wednesday
3. Wednesday and Thursday
4. Thursday and Friday
5. Friday and Saturday
6. Saturday and Sunday
7. Sunday and Monday
Of these seven equally likely cases, only the last
two are favourable. Hence, the required probability
is 2/7.
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