Probability

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

Explanation: Here, S = {1, 2, 3, 4, ...., 19, 20}. Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}. P(E) = n(E)/n(S) = 9/20.

There are 5 green 7 red balls. Two balls are selected one by one without replacement. Find the probability that first is green and second is red.

P (G) × P (R) = (5/12) x (7/11) = 35/132

Find the probability of getting a numbered card when a card is drawn from the pack of 52 cards.

Total Cards = 52. Numbered Cards = (2, 3, 4, 5, 6, 7, 8, 9, 10) 9 from each suit 4 × 9 = 36P (E) = 36/52 = 9/13

What is the probability of getting a sum of 7 when two dice are thrown?

Total number of ways = 6 × 6 = 36 ways. Favorable cases = (1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3) --- 6 ways. P (A) = 6/36 = 1/6

Using a six-sided die, Carlin has rolled a six on each of 4 successive tosses. What is the probability of Carlin rolling a six on the next toss? 1/2 1/4 1/6 1/30 1/3125

Answer: 1/6 Explanation: The outcomes of previous rolls do not affect the outcomes of future rolls. There is one desired outcome and six possible outcomes. The probability of rolling a six on the fifth roll is 1/6, the same as the probability of rolling a six on any given individual roll.

If a bag of balloons consists of 47 white balloons, 5 yellow balloons, and 10 black balloons, what is the approximate likelihood that a balloon chosen randomly from the bag will be black? 19% 16% 21% 33%

Answer: 16% Explanation: First, calculate the total number of balloons in the bag: 47 + 5 + 10 = 62. Ten of these are black, so divide this number by 62. Then, multiply by 100 to express the probability as a percentage: 10 / 62 = 0.16 0.16 100 = 16%

In a lottery game, there are 2 winners for every 100 tickets sold on average. If a man buys 10 tickets, what is the probability that he is a winner? 21.5% 20% 18.3% 2%

Answer : 18.3% Explanation : First, simplify the winning rate. If there are 2 winners for every 100 tickets, there is 1 winner for every 50 tickets sold. This can be expressed as a probability of 1/50 or 0.02. In order to account for the (unlikely) scenarios of more than a single winning ticket, calculate the probability that none of the tickets win and then subtract that from 1. There is a probability of 49/50 that a given ticket will not win. For all ten to lose that would be (49/50)^(10) ≈ 0.817. Therefore, the probability that at least one ticket wins is 1 − 0.817 = 0.183 or about 18.3%

A two-digit number is chosen at random. What is the probability that the chosen number is a multiple of 7? 1/10 1/9 11/90 12/90 13/90

Answer: 13/90 Explanation: There are 90 two-digit numbers (all integers from 10 to 99). Of those, there are 13 multiples of 7: 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98.

A bag contains 14 blue, 6 red, 12 green, and 8 purple buttons. 25 buttons are removed from the bag randomly. How many of the removed buttons were red if the chance of drawing a red button from the bag is now 1/3? 0 1 3 5 6

Answer: 1 Explanation: Add the 14 blue, 6 red, 12 green, and 8 purple buttons to get a total of 40 buttons. If 25 buttons are removed, there are 15 buttons remaining in the bag. If the chance of drawing a red button is now 1/3, then 5 of the 15 buttons remaining must be red. The original total of red buttons was 6. So, one red button was removed.

An MP3 player is set to play songs at random from the fifteen songs it contains in memory. Any song can be played at any time, even if it is repeated. There are 5 songs by Band A, 3 songs by Band B, 2 by Band C, and 5 by Band D. If the player has just played two songs in a row by Band D, what is the probability that the next song will also be by Band D? 1 in 5 1 in 3 1 in 9 1 in 27 Not enough data to determine.

Answer: 1 in 3 Explanation : The probability of playing a song by a particular band is proportional to the number of songs by that band divided by the total number of songs, or 5/15=1/3 for B and D. The probability of playing any particular song is not affected by what has been played previously, since the choice is random and songs may be repeated.

A regular deck of cards has 52 cards. Assuming that you do not replace the card you had drawn before the next draw, what is the probability of drawing three aces in a row? 1 in 52 1 in 156 1 in 2000 1 in 5525 1 in 132600

Answer: 1 in 5525 Explanation : The probability of getting three aces in a row is the product of the probabilities for each draw. For the first ace, that is 4 in 52 or 1 in 13; for the second, it is 3 in 51 or 1 in 27; and for the third, it is 2 in 50 or 1 in 25. So the overall probability, P, is P=1/13*1/17*1/25=1/5,525

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green? A. 1/3 B. 3/4 C. 7/19 D. 8/21 E. 9/21

Answer: 1/3 Explanation: Total Number of balls = 8+7+6 =21 Probability of neither red or green = 7/21

Three coins are tossed up in the air, one at a time. What is the probability that two of them will land heads up and one will land tails up? 0 1/8 1/4 3/8

Answer: 3/8. Explanation: Shown below is the sample space of possible outcomes for tossing three coins, one at a time. Since there is a possibility of two outcomes (heads or tails) for each coin, there is a total of 2*2*2=8 possible outcomes for the three coins altogether. Note that H represents heads and T represents tails: HHH HHT HTT HTH TTT TTH THT THH Notice that out of the 8 possible outcomes, only 3 of them (HHT, HTH, and THH) meet the desired condition that two coins land heads up and one coin lands tails up. Probability, by definition, is the number of desired outcomes divided by the number of possible outcomes. Therefore, the probability of two heads and one tail is 3/8, Choice D.

There are 6 blue marbles, 3 red marbles, and 5 yellow marbles in a bag. What is the probability of selecting a blue or red marble on the first draw? 1/3 4/7 8/14 9/14 11/14

Answer: 9/14 Explanation: Use this ratio for probability: Probability = Number of Desired Outcomes Number of Possible Outcomes There are 6 blue marbles and 3 red marbles for a total of 9 desired outcomes. Add the total number of marbles to get the total number of possible outcomes, 14. The probability that a red or blue marble will be selected is 9/14.

On a six-sided die, each side has a number between 1 and 6. What is the probability of throwing a 3 or a 4? 1 in 6 1 in 3 1 in 2 1 in 4

Correct answer: 1 in 3. Explanation: On a six-sided die, the probability of throwing any number is 1 in 6. The probability of throwing a 3 or a 4 is double that, or 2 in 6. This can be simplified by dividing both 2 and 6 by 2. Therefore, the probability of throwing either a 3 or 4 is 1 in 3.

Charlie is going to roll a die and flip a coin. What is the probability that he will roll a 6 and the coin will land with heads facing up? 1/6 1/12 1 1/3

Correct answer: 1/12 Explanation: There is only one way to roll a 6 and for the coin to land on heads; thus, the probability is 1/12

A coin is thrown 3 times .what is the probability that atleast one head is obtained?

Sample space = [HHH, HHT, HTH, THH, TTH, THT, HTT, TTT]Total number of ways = 2 × 2 × 2 = 8. Fav. Cases = 7P (A) = 7/8ORP (of getting at least one head) = 1 - P (no head)⇒ 1 - (1/8) = 7/8

1 card is drawn at random from the pack of 52 cards.(i) Find the Probability that it is an honor card.(ii) It is a face card.

honor cards = (A, J, Q, K) 4 cards from each suits = 4 × 4 = 16P (honor card) = 16/52 = 4/13(ii) face cards = (J,Q,K) 3 cards from each suit = 3 × 4 = 12 Cards.P (face Card) = 12/52 = 3/13