急! F5 Probability 5q7

25.
(b)
To draw socks of the same colour, the worst case is that 1 black sock and 1white sock are drawn in the first two draws. Then, no matter what colour thethird sock is, there must be socks of the same colour.

Hence, number of socks drawn at least = 3

(c)
To draw a black sock, the worst case is that 6 white socks are drawn in the firstsix draws. Then, the seventh sock drawn must be black.

Hence, number of socks drawn at least = 7


31.
Number of ways that the 8 children lined up randomly
= 8P8
= 8!
= 40320

Number of ways that all boys are in one end and all girls are in the other end
= 3P3 x 5P5
= 3! x 5!
= 720

The required probability
= 720/40320
= 1/56


32.
(a)
Number of ways that the books are put randomly
= 6P6
= 6!
= 720

Number of ways that the books are put in correct order
= 1

The required probability
= 1/720

(b)
Number of ways that Book 1 and Book 2 are next to each other
= 5P5 x 2P2
= 5! x 2!
= 240

The required probability
= 240/720
= 1/3

(c)
Number of ways that Book 1 is put on the left end
= 1P1 x 5P5
= 1 x 120
= 120

The required probability
= 120/720
= 1/6