15 Girls are placed at random in a line. What is the probability that theTwo youngest girls are together.Two youngest girls are not together

1. 15 Girls are placed at random in a line.
What is the probability that the
Two youngest girls are together.
Two youngest girls are not together.
NADEEM UDDIN
ASSOCIATE PROFESSOR
OF STATISTICS
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2. Example
15 Girls are placed at random in a line. What is the
probability that the
(i)Two youngest girls are together.
(ii)Two youngest girls are not together.
Solution
𝑛 𝑠 = 15!

3. (i) Let A be the event the two youngest girls are together,
Consider two youngest girls together as one item.
So there are 14 items to arrange, these 14 items can be
arrange in 14! Ways.
The two youngest can be arranged in two ways,
Therefore 𝑛 𝐴 = 2 × 14!
𝑝 𝐴 =
𝑛 𝐴
𝑛 𝑠
=
2 × 14!
15!
=
2
15
= 0.133
(ii) Where A′ is the event that two youngest girls are not together.
𝑝 A′ = 1 − 𝑝 𝐴
𝑝 A′ = 1 − 0.133 = 0.867