is this an accurate answer to the question ? help me correct it and mae sure it is accurate 100%. thanks

wri your own three-part probability question and provide a solution. In your question, wrie a scenario for each of the following: Probability of A and B happening, where A and B are independent events. Probability of A or B or C happening, where A, B, and C are independent events. Probability of A happening at least once in N triesPart 1:

• Scenario: A coin is flipped twice. What is the probability that both flips result in heads?
• Solution:
  • Since the flips are independent events, we can calculate the probability by multiplying the individual probabilities.
  • The probability of heads on a single flip is 1/2.
  • So, the probability of getting heads on both flips is (1/2) x (1/2) = 1/4.

Part 2:

• Scenario: A lottery has 5 numbers. A player chooses 3 numbers. What is the probability that the player's chosen numbers match at least one of the numbers drawn by the lottery?
• Solution:
  • Let A be the event that the player's first chosen number matches a drawn number.
  • Let B be the event that the player's second chosen number matches a drawn number.
  • Let C be the event that the player's third chosen number matches a drawn number.
  • Since the draws are independent events, A, B, and C are independent.
  • The probability of each individual match is 1/5.
  • So, the probability of at least one match is 1 - P(A' AND B' AND C')
  • where P(A' AND B' AND C') is the probability that none of the chosen numbers match any of the drawn numbers.
  • To find P(A' AND B' AND C'), we calculate the probability of all three events not happening and subtract from 1.
  • P(A' AND B' AND C') = (4/5) x (4/5) x (4/5) = 64/125
  • So, the probability of at least one match is 1 - 64/125 = 61/125.

Part 3:

• Scenario: A fair six-sided die is rolled. What is the probability that the die shows a 1 at least once in 10 rolls?
• Solution:
  • Let A be the event that the die shows a 1 on the first roll.
  • Let B be the event that the die shows a 1 on the second roll.
  • Let C be the event that the die shows a 1 on the third roll.
  • Let so on, up to the tenth roll.
  • Since each roll is an independent event, A, B, C, ... are independent.
  • The probability of getting a 1 on any single roll is 1/6.
  • The probability of getting a 1 at least once in 10 rolls is the complement of the probability of not getting a 1 at all in 10 rolls.
  • To find the probability of not getting a 1 at all in 10 rolls, we calculate the probability of all 10 rolls not showing a 1 and subtract from 1.
  • P(A' AND B' AND C' ... Z') = (5/6) x (5/6) x (5/6) x ... x (5/6) = (5/6)^10
  • So, the probability of getting a 1 at least once in 10 rolls is 1 - (5/6)^10.