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Probability!. Note: Exclamation Point above i s being used to i ndicate “Excitement,” not Factorial. It’s about time… M408 Probability unit. Probability – the chance of a particular random event occurring.
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Probability! Note: Exclamation Point above is being used to indicate “Excitement,” not Factorial. It’s about time… M408 Probability unit
Probability – the chance of a particular random event occurring. • If ‘A’ is a particular event that could happen in a general situation, the probability of ‘A’ is notated as P(A). • If P(A) = 0, then event ‘A’ is not possible (never happens) • If P(A) = 1, then event ‘A’ is certain to happen (always happens) • Sample Space: a list or picture of all possible outcomes that could occur.
Standard Deck of Cards 52 total cards: 26 black 26 red 4 suits: clubs spades hearts diamonds 13 13 13 13 13 kinds: Ace, 2, 3,…, 10, Jack, Queen, King (face cards)
Ex 1 – you pick one card at random from a standard deck. • A.) What is the sample space? • B.) P(red jack) • C.) P(face card) • D.) P(black non-face card) • E.) P(value of 8 or less) --- Assume Ace counts as ‘1’ • F.) P(green card) • G.) P(red or black card) • H.) P(club) • I.) P(spade or diamond)
Ex 2 – A coin is tossed three times. • A.) Draw the sample space. • B.) P(exactly two heads) • C.) P(two or more tails) • D.) P(no more than one heads)
Ex 3 – A standard six-sided die is rolled. • A.) P(roll a 4) • B.) P(roll a primenumber) • C.) P(roll a 7)
Ex 4 – You roll one red die and one green die at the same time. • A.) Draw the sample space. • B.) P(roll a sum of 11) • C.) P(both dice land with the same number facing up) • D.) P(roll a sum greater than or equal to 7) • E.) P(sum is a multiple of 2 or 3)
Ex 5 – You have 3 orange kittens, 4 tabby kittens, and 8 siamese kittens. Meow! • A.) If you pick two kittens at random, what is the probability that they are both siamese? • B.) If you pick five kittens, what is the probability of picking 2 orange kittens and 3 siamese kittens? • C.) If you pick 6 kittens, what is the probability that at least 4 are siamese?
Compound probabilities - • Now we will study probabilities of separate events happening at the same time. The following expressions will be important. • : probability that both events happen. • : probability that one, or the other, or possibly both events happen.
Independent events – do not affect each other. • If events ‘A’ and ‘B’ are independent, then P(A) is not affected by P(B), or vice versa. • To find the probability of Independent events A and B both happening: • same as • Note: The formula is very easy to remember, but it ONLY applies if you know the events are INDEPENDENT!
Ex 6 – pick a card from a standard deck. Replace the card, shuffle, then pick again. • A.) Are the two picks independent? • B.) What is the probability of picking a club on your first pick, AND picking a queen on your second pick?
Ex 7 – • A.) What is the probability of rolling a die twice in a row, and getting a ‘3’ both times? • B.) What is the probability of rolling three even numbers in a row?
Ex 8 – • You get asked to babysit for the neighbors on 40% of school days. 4 out of 5 days, the baby wants to eat spaghetti. The baby spills food on 60% of the days. If these events are all independent of each other, what is the probability that today you get asked to babysit, AND the baby spills spaghetti?
