Probability of intersection

Three students have a probability of 0.7,0.5 and 0.4 to graduated from university respectively. What is the probability that at least one of them will be graduated?

Correct result:

p =  0.91

Solution:

$p_{1}=0.7 \ \\ p_{2}=0.5 \ \\ p_{3}=0.4 \ \\ \ \\ p=p_{1}+p_{2}+p_{3} - p_{1} \cdot \ p_{2}-p_{2} \cdot \ p_{3}-p_{3} \cdot \ p_{1} + p_{1} \cdot \ p_{2} \cdot \ p_{3}=0.7+0.5+0.4 - 0.7 \cdot \ 0.5-0.5 \cdot \ 0.4-0.4 \cdot \ 0.7 + 0.7 \cdot \ 0.5 \cdot \ 0.4=\dfrac{ 91 }{ 100 }=0.91$

Try another example

Showing 0 comments:

Next similar math problems:

• Fall sum or same
  Find the probability that if you roll two dice, it will fall the sum of 10, or the same number will fall on both dice.
• Double probability
  The probability of success of the planned action is 60%. What is the probability that success will be achieved at least once if this action is repeated twice?
• Candies
  In the box are 12 candies that look the same. Three of them are filled with nougat, five by nuts, four by cream. At least how many candies must Ivan choose to satisfy itself that the selection of two with the same filling? ?
• Cards
  Suppose that are three cards in the hats. One is red on both sides, one of which is black on both sides, and a third one side red and the second black. We are pulled out of a hat randomly one card and we see that one side of it is red. What is the probabi
• Three shooters
  Three shooters shoot, each one time, on the same target. The first hit the target with a probability of 0.7; second with a probability of 0.8 and a third with a probability of 0.9. What is the probability to hit the target: a) just once b) at least once c
• Probabilities
  If probabilities of A, B and A ∩ B are P (A) = 0.62 P (B) = 0.78 and P (A ∩ B) = 0.26 calculate the following probability (of union. intersect and opposite and its combinations):
• Lottery
  Fernando has two lottery tickets each from other lottery. In the first is 973 000 lottery tickets from them wins 687 000, the second has 1425 000 lottery tickets from them wins 1425 000 tickets. What is the probability that at least one Fernando's ticket
• Today in school
  There are 9 girls and 11 boys in the class today. What is the probability that Suzan will go to the board today?
• Shooters
  In army regiment are six shooters. The first shooter target hit with a probability of 49%, next with 75%, 41%, 20%, 34%, 63%. Calculate the probability of target hit when shooting all at once.
• Class - boys and girls
  In the class are 60% boys and 40% girls. Long hair has 10% boys and 80% girls. a) What is the probability that a randomly chosen person has long hair? b) The selected person has long hair. What is the probability that it is a girl?
• Win in raffle
  The raffle tickets were sold 200, 5 of which were winning. What is the probability that Peter, who bought one ticket will win?
• The dice
  What is the probability of events that if we throw a dice is rolled less than 6?
• Birth
  Let's assume that the probability of the birth of a boy and a girl in the family is the same. What is the probability that in a family with five children, the youngest and oldest child is a boy?
• Probability
  What are the chances that the lottery, in which the numbers are drawn 5 of 50 you win the first prize?
• Balls
  The urn is 8 white and 6 black balls. We pull 4 randomly balls. What is the probability that among them will be two white?
• Glasses
  There are 36 pupils in the class. Nine girls wear glasses. Boys with glasses are five less than girls without glasses. Boys without glasses are two times more than girls without glasses. How many boys and how many girls?
• Median
  The number of missed hours was recorded in 11 pupils: 5,12,6,8,10,7,5,110,2,5,6. Determine the median.