probability?

1.
In the 52 playing cards, there are 4 suits.
Thus, there are 4 'jacks' and 4 'queens'.

P([1st card is a 'jack'] and P(2nd card is a 'queen')
= (4/52) × (4/52)
= (1/13) × (1/13)
= 1/169


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2.
(a)
W : a white ball
G : a green ball
B : a blue ball
Total number of balls = 2 + 4 + 3 = 9

P(W) = P(a white ball) = 2/9
P(G) = P(a green ball) = 4/9
P(B) = P(a blue ball) = 3/9

P(3 green balls)
= P(GGG)
= P(G) × P(G) × P(G)
= (4/9)³
= 64/729

(b)
P(2 white balls and 1 green ball)
= P(WWG or WGW or GWW)
= P(WWG) + P(WGW) + P(GWW)
= (2/9) × (2/9) × (4/9) + (2/9) × (4/9) × (2/9) + (4/9) × (2/9) × (2/9)
= (16/729) × 3
= 16/243

(c)
P(3 balls have the same colour)
= P(WWW) + P(GGG) + P(BBB)
= (2/9)³ + (4/9)³ + (3/9)³
= (8/729) + (64/729) + (27/729)
= 99/729
= 11/81


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3.
(a)
P(late on a particular day)
= P([traffic jam and late] or [no traffic jam and late])
= (5/8) × (4/5) + [1 - (5/8)] × (1/9)
= (1/2) + (1/24)
= (12/24) + (1/24)
= 13/24

(b)
P(late on a particular day)
= P([late on particular day 1] and [late on particular day 2])
= P(late on particular day 1) × P(late on particular day 2)
= (13/24) × (13/24)
= 169/576