independent events

what’s the probability of rolling a 5 and then rolling a number less then 2 Roll a 5: There's only one 5 on a six sided die P(X = 5) = 1/6 A number less than 2 is only 1: P(X < 2) = P(X = 1) P(X = 1) = 1/6 Since each event is independent, we multiply: P(X = 5) * P(X = 1) = 1/6 * 1/6 P(X = 5)...

A box contains 6 yellow, 3 red, 5 green, and 7 blue colored pencils. A pencil is chosen at random, it is not replaced, then another is chosen. What is the probability of choosing a red followed by a green? We have 6 + 3 + 5 + 7 = 21 total pencils P(Red on the first draw) = Total Red / Total...

A die and a coin are tossed. What is the probability of getting a 6 and a tail? Roll a 6: P(6) = 1/6 Flip a tail: P(T) = 1/2 Probability of getting a 6 and a tail: Since both events are independent, we have: P(6 and T) = P(6) * P(T) P(6 and T) = 1/6 * 1/2 P(6 and T) = 1/12

A spinner has 3 equal sections labelled A, B, C. A bag contains 3 marbles: 1 grey, 1 black, and 1 white. The pointer is spun and a marble is picked at random. a) Use a tree diagram to list the possible outcomes. A, Grey A, Black A, White B, Grey B, Black B, White C, Grey C, Black C, White...

Suppose that 18% of people own dogs. If you pick two people at random, what is the probability that they both own a dog? Since each person is independent of the others, we have: P(Person 1 has a dog and person 2 have a dog) = P(person 1 has a dog) * P(person 2 has a dog) P(Person 1 has a dog...

Taylor is playing a game using a die and a spinner. The spinner is divided into 4 equal parts with colors green, red, yellow, and purple. Taylor rolls the die and spins the spinner. What is the probability the die shows a 2 and the spinner lands on purple? Probability of rolling a 2 on the die...

If 4 people have the same 7 shirts, what is the chance that they will wear the same shirt on one day? For each person, the probability they all wear the first shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 For each person, the probability they all wear the second shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256...

A box contains 5 plain pencils and 7 pens. A second box contains 4 color pencils and 4 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected? Probability of plain pencil from first...