#1. The probability of flipping a coin 5 times and having all five flips be heads is a favorable 1 out of possible 2, done five times. The fraction 1/2 • 1/2 • 1/2 • 1/2 • 1/2 = 1/32 which is 3.125%
#2. The probability of rolling a die and having a 6 come up 5 times in a row is a Favorable 1 (there is only 1 – six on a die) out of Possible 6 (there are six options on a die) happening five (5) times in a row. 1/6 • 1/6 • 1/6 • 1/6 • 1/6 = 1/7,776 or 0.013%
#3. The probability of rolling two dice and getting a total score of a three would be first looking at all the options when rolling two dice and the determining how many of those would be Favorable options of a score of three (3). Once this Favorable count is determined, write it out of the number of Possible outcomes. This probability then would need to be used as a factor four (4) times.
#4. P(Ace, Ace) if a Favorable ace happens four (4) times in a deck of a Possible 52 cards, then the probability is 4/52 reducing to 1/13. This though is being asked to happen in each of two (2) decks. Therefore, the probability of P(Ace, Ace) is 1/13 • 1/13 = 1/169 or 0.59% of the time.
$5. P(Heads, 6, King of Hearts) is a Favorable over Possible outcome for each of the three (3) events. How many Heads out of Possible outcomes on a coin? How many sixes (6) out of Possible outcomes on a dice? How many Favorable King of Hearts out of Possible outcomes in a deck of cards?
#6. P(matching pair) but this may be more easily understood if said P(card, match). The Favorable first card could be how many? The Possible outcomes for that first card is how many? Then, for the “match,” how many Favorable matches are there in the second deck to the first card? Out of how many Possible for that “match” in the second deck?
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