1a. Two independent events could be flipping a coin to get heads and rolling a single die to get 4.
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1b. They are independent because one item does not touch the other to affect the outcome.
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1c. The probability of heads is 1/2 as there's 1 side out of 2 total. The probability of getting a 4 is 1/6 as there's one "4" out of six sides total. The probability the two events happen at the same time is 1/2 * 1/6 = 1/12. We can multiply like this because the two events are independent
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2a. Two dependent events could be picking an ace from the deck of cards, not putting it back, and selecting another ace from the same deck.
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2b. We know this is dependent because the second selection's probability changes based on the first selection. This is entirely because the card was not put back.
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2c. Selecting an ace has probability 4/52 = 1/13. We have not put the card back, so we have 4-1 = 3 aces left and 52-1 = 51 cards overall. The probability of getting another ace is 3/51, which is different from 4/52. If we put the card back, then it would be 4/52. The probability of getting two aces in a row, after not putting the first card back, is (4/52)*(3/51) = 12/2652 = 1/221. So as you can see, this is different from the independent section above in that we didn't simply say (4/52)*(4/52), but instead wrote (4/52)*(3/51).
