Statistics Independent Events

[Music] welcome back to moomoomath today we're going to look at independent and dependent events so i'm going through our note taking guide okay independent and dependent events these are and problems and in math and problems one f event occurs and a second event occurs we are not going to add we're actually going to multiply so and we always think of in math as adding but we don't and the way to remember that in probability is this do not add d do not add okay so it's kind of an acronym to help us remember we don't add we end up multiplying so you're going to multiply the two probabilities together when you see and which is the intersection of two events okay so event a occurs occurring does not affect the probability of event b that's an independent event so if you flip a coin and then you draw a card they don't affect each other or if you flip a coin and then pick it up again and flip it again the first event doesn't affect the second event so those are independent events events that don't affect each other okay so let's look at some examples of independent events a coin is tossed and a six-sided dice is rolled so as you can see the the coin toss and the rolling of the dice they don't affect each other find the probability of landing on a head on the coin and rolling a three on the die okay so what's the probability of landing on a head well we have heads and tails so we have two choices so getting a head is one out of two and we're going to multiply that times because it's an and problem so do not add multiply rolling a three on a dice well three on a die is one chance out of six because we have six sides on a die so we're going to multiply that together and that just gives us 1 12. so that's the probability of that event occurring okay let's look at another one a card is chosen at random from a deck of 52 cards if it then is replaced and a second card is chosen what's the probability of choosing a jack and an eight okay well the probability of choosing a jack we have four jacks in the deck and we have 52 cards and then it's an and problem so we're going to multiply and then at 8 well we have 4 8 out of 52 and we replace the cards so we still have 52 cards to choose from so i'm just going to reduce these before i multiply them this is going to be 1 13 times 1 13 which is 1 out of 169 and that would be my probability okay so let's look at the next one a jar contains three red five green two blue and six yellow marbles so marbles chosen at random from the jar after replacing it so you replace it a second marble's chosen what's the probability of choosing a green and a yellow okay so replacement when you do replacement that is independent independent means if the first event doesn't affect the second one so you have the same number of marvels to choose from so what's the probability of choosing the green well green we have 5 out of let's see that's 8 9 10 out of 16 times and means do not add multiply yellow yellow is 6 6 out of 16. now i'm going to go ahead and reduce 5 16 doesn't reduce but this reduces to 3 8. now i can multiply and i can get 15 out of what's 16 times 8 16 times 8 is 128 so there is my probability okay 15 out of 128 a school survey found that 9 out of 10 students like pizza if three are of these are chosen at random with replacement what's the probability that all three students like pizza okay our first one is our first chance is a nine out of ten we have nine chances out of ten but then we do it a second time and we put the same kids back in the dar and choose again and third one same probability so we have three events occurring so we have to multiply that together that gives us nine times nine times nine which is i should know that 729 out of 1000 and that would be our probability 729 times out of a thousand tries we would get all three people like [Music] you