probability

Of the 20 boats at the Mariana, 10 were from Massachusetts. What is the probability that a randomly selected boat will be from Massachusetts? P(Boat from Massachusetts) = Number of Massachusetts boats / Total Boats at the Mariana P(Boat from Massachusetts) = 10/20 Simplifying this fraction, we...

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 fake coin has heads on both sides, if the coin tossed once, what is the probability of getting a head? Since you always flip a head, we have: P(Head) = 1 or 100%

A group of people were asked if they had run a red light in the last year. 497 responded "yes", and 223 responded "no". Find the probability that if a person is chosen at random, they have run a red light in the last year. P(Run Red Light) = yes answers / total answers P(Run Red Light) = 497 /...

Sarah rolls 2 fair dice and adds the results from each. Work out the probability of getting a total that is a factor of 6. Factors of 6 are {6, 12} P(Roll a 6) = 5/36 P(Roll a 12) = 1/36 P(Roll a 6 or Roll a 12) = P(Roll a 6) + P(Roll a 12) P(Roll a 6 or Roll a 12) = 5/36 + 1/36 P(Roll a 6 or...

assume your math class has 10 sophomores and 7 juniors. there are 3 female sophomores and 4 male juniors. what is the probability of randomly selecting a student who is a female or a junior Sophomores: 10 sophomores: 3 female male = 10 - 3 = 7 Juniors: 7 juniors 4 males female = 7 - 4 = 3...

A computer randomly generates a whole number from 1 to 25. Find the probability that the computer generates a multiple of 5 Multiples of 5: {1, 5, 25} So we have the probability of a random number multiple of 5 is 3/25

A 6-sided die is rolled once. What is the probability of rolling a number less than 4? Using our one dice calculator, we get: P(N < 4) = 1/2

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...

A bowler knocks down at least 6 pins 70 percent of the time. Out of 200 rolls, how many times can you predict the bowler will knock down at least 6 pins? Expected Value of (knocking down at least 6 pins) = number of rolls * probability of knocking down at least 6 pins Expected Value of...

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...

If you toss a fair coin 6 times, what is the probability of getting all tails? We type in our search engine TTTTTT and we get: P(TTTTTT) = 1/64 or 0.015625

Given P(A) = 0.37, find P ( not A ) Not A is also written as A'. We use the formula below: P(A') = 1 - P(A) P(A') = 1 - 0.37 P(A') = 0.63

a card selected from a deck of 52 cards what is the probability it is a black card or face card Facts: Half the cards in the deck are black (26/52) There are 12 face cards (K, Q, J) in a deck (12/52) Black and Face = 6/52 (Duplicates from above) P(Black or Face) = P(Black) + P(Face) - P(Black...

The chance of a soldier being an enemy spy is .0005. Out of 10,000 soldiers, how many of them are expected to be spies? Expected Spies = Probability of being a spy * Total Soldiers Expected Spies = 0.0005 * 10000 Expected Spies = 5

A box contains 5 black and 2 white balls. 2 balls are drawn without replacement. Find the probability of drawing 2 black balls. First draw probability of black is: Total Balls in box = Black balls + white balls Total Balls in Box = 5 + 2 Total Balls in Box = 7 P(Black) = Black Balls / Total...

Refer to a bag containing 13 red balls numbered 1-13 and 5 green balls numbered 14-18. You choose a ball at random. a. What is the probability that you choose a red or even numbered ball? b. What is the probability you choose a green ball or a ball numbered less than 5? a. The phrase or in...

A dice has six sides. The dice is rolled once. What is the probability that a six will be the result. P(6) = 1/6

A fuel injection system is designed to last 18 years, with a standard deviation of 1.4 years. What is the probability that a fuel injection system will last less than 15 years? Using our z-score calculator, we see that: P(X < 15) = 0.416834