probability

Oliver rolls a fair six-sided dice and spins a fair three-sided spinner with equal-sized sections labelled 1,4 and 8. He adds the results together. What is the probability that the total he scores is greater than 8? Give your answer as a fraction in its simplest form. Setup the sample space...

Two dice are rolled. Determine the probability of the following. Rolling an even number or a number greater than 6 We want P(X = Even) or P(X>6) With 2 dice, our die totals are: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Evens are: 2, 4, 6, 8, 10, 12 > 6 = 7, 8, 9, 10, 11, 12 When the problem states...

On your first draw, what is the probability of drawing a red card, without looking, from a shuffled deck containing 6 red cards, 6 blue cards, and 8 black cards? P(Red) = Total Red / Total Cards P(Red) = 6 red/(6 red + 6 blue + 8 black) P(Red) = 6/20 This fraction can be simplified. The...

Three ordinary dice are rolled. What is the probability that the results are all less than 5 Calculate individual die probabilities: Die 1 P(x < 5) = 4/6 = 2/3 Die 2 P(x < 5) = 4/6 = 2/3 Die 3 P(x < 5) = 4/6 = 2/3 Since each roll is independent, we have: P(Die 1 < 5, Die 2 < 5, Die 3 < 5) =...

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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 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,,8,9,10,11,12}. Find the probability of rolling a number less than 6. We want a {1, 2, 3, 4, 5} P(X < 6) = 5/12

When five people are playing a game called hearts, each person is dealt ten cards and the two remaining cards are put face down on a table. Because of the rules of the game, it is very important to know the probability of either of the two cards being a heart. What is the probability that at...

If a die is rolled, what is the probability that the number rolled will not be a "5"? Possible rolls: {1, 2, 3, 4, 5, 6} Probability of not a 5 means: {1, 2, 3, 4, 6} P(Not 6) = 1 - P(6) P(Not 6) = 1 - 1/6 P(Not 6) = 5/6

An eccentric millionaire decided to give away $1,000,000 if Janelle took one die and rolled a "4". He wanted Janelle to have a better than 1 in 6 chance of winning, so before she rolled the die he told her that she could roll the die 3 times. If any roll was a "4", she would win the million...

If the probability of winning is X, what is the probability of losing? (Assume there are no ties.) This means you can either win or lose. Since all probabilities in the sample space must add up to 1, then we have: P(Winning) + P(Losing) = 1 P(Losing) = 1 - P(Winning) Since P(Winning) = X, we...

Larry is rolling two dice. His dad told him that he can skip doing the dishes that night unless he rolls double sixes. What is the probability that Larry will be able to skip doing the dishes? P(6, 6) = 1/6 * 1/6 = 1/36 P(Not 6,6) = 1 - 1/36 = 35/36

If the probability of getting struck by lighting each year is 1 in 1,000,000, what is the probability that you will not be struck by lightning in one year? Our sample space is either getting struck by lightning or NOT getting struck by lightning. So we have: P(Not getting struck by lightning) =...

If two coins are flipped, what is the probability that there will not be two heads? There's only one way to flip 2 coins and get 2 heads: P(HH) = 1/2 * 1/2 = 1/4 Which means the probability of NOT getting 2 heads is: 1 - 1/4 = 3/4

A bag has 3 red, 5 blue, and 2 yellow pieces of candy. What is the theoretical probability of drawing a blue piece of candy P(Blue) = Blue Candies / Total Candies P(Blue) = 5 / (3 + 5 + 2) P(Blue) = 5 / 10 We can simplify this using our GCF calculator and we get: P(Blue) = 1/2

The letters that form the word ALGEBRA are placed in a bowl. What is the probability of choosing a letter that is not “A”? ALGEBRA has 7 letters Of the 7 letters, we have 2 A's. So we have 7 - 2 = 5 letters which are not A P(Not A) = Letters not A / Total letters P(Not A) = 5/7

A pet store has 10 rabbits. What’s the probability that they have at least 1 female rabbit. At least 1 female rabbit means we must have a female rabbit First, we calculate the probability of 0 females A rabbit can be either male or female with equal probabilities of 1/2 or 0.5. Since each...

mark has a drawer full of 12 yellow baseball caps and 18 white baseball caps. What is the probability of the next cap he chooses at random will be yellow? P(yellow) = yellow caps / Total caps P(yellow) = 12/(12 + 18) P(yellow) = 12/30 Simplifying this fraction, we get: P(yellow) = 2/5

A pair of dice are rolled. Find the probability for P(Not 2 or Not 12). P(Not 2 or Not 12) = 1 - P(2) - P(12) P(Not 2 or Not 12) = 1 - 1/36 - 1/36 P(Not 2 or Not 12) = 34/36 P(Not 2 or Not 12) = 17/18

a 12 sided die is rolled find the probability of rolling a number greater than 7 We assume this is a fair die, not loaded. This means each side 1-12 has an equal probability of 1/12 of being rolled. The problem asks, P(Roll > 7) Greater than 7 means our sample space is {8, 9, 10, 11, 12} If...