(a) Flipping a coin and getting heads, then flipping it again and getting tails
Ans: Independent. Flipping heads the first time does not mean that the coin will be more/less likely to land tails the second time. The chances are still 1/2.
(b) Rolling doubles with two dice, then rolling doubles again.
Ans: Independant. Rolling doubles the first time does not make it more/less likely that a double will be rolled a second time. The dice cannot "remember" its previous result and change the next result.
(c) Drawing (and removing) two aces from a normal deck cards, then drawing kings.
Ans: Dependant. After removing the 2 aces, there are less cards in the deck, so the deck "remembers" that 2 aces are already picked, so it is more likely that a king will be picked.
(d) Drawing (and removing) a red ball initially containing two red balls and three white balls, then drawing a white ball.
Ans: Dependent. After removing the first red ball, there are less balls in the bag, so there is a higher chance of picking a white ball.
Mini Task 5:
(a) 13/100 x 8/100 = 13/1250
(b) 1/6 x 1/6 = 1/36
(c) 1/52 x 1/52 = 1/2704
(d) 1/100 x 1/100 = 1/10000
P(Getting heads 3 times in 3 tosses)
= 1/2 x 1/2 x 1/2