Explanation:
Event A is a certain event because with 14 girls and only 12 months in a year, by the pigeonhole principle, there must be at least two girls who were born in the same month.
Event B is an elementary event because there is only one part labeled with the number 10 out of 75 parts in the box, so the probability of drawing that part is 1/75.
The relative frequency of hits is calculated by dividing the number of hits by the total number of shots. In this case, it is 20/25.
The relative frequency of boys born in that month is calculated by dividing the number of boys born by the total number of births. In this case, it is 43/100.
There are four balls labeled with numbers divisible by 3 (3, 6, 9, and 12) out of twelve balls in total. So the probability of drawing a ball with a number divisible by 3 is 4/12 = 1/3.
The probability that a part is not of good quality is equal to 1 minus the probability that it is of good quality. In this case, it is 1 - 0.75 = 0.25.
The probability that at least one coin lands heads up is equal to 1 minus the probability that both coins land tails up. The probability that both coins land tails up is (1/2) * (1/2) = 1/4. So the probability that at least one coin lands heads up is 1 - 1/4 = 3/4.
A fair die has six equally likely outcomes when rolled. So the probability of rolling a 2 is 1/6.
A deck of cards containing 36 cards has four suits: clubs, diamonds, hearts, and spades. Each suit has nine cards, so there are nine spades in the deck. So the probability of drawing a spade is 9/36 = 1/4.
There are two white marbles and ten marbles in total in the bag. So the probability of randomly selecting a white marble is 2/10 = 1/5.
There are four ways to roll two dice and get a sum of five: (1,4), (2,3), (3,2), or (4,1). Each outcome has a probability of (1/6) * (1/6) = 1/36. So the probability that the sum of the numbers rolled is five is 4 * (1/36) = 1/9.
If Jānis throws a ball into the basket with a probability of 0.68 and he makes 50 throws, we can expect him to throw the ball into the basket about 0.68 * 50 = 34 times.
The probability that at least one die shows four points when two dice are rolled can be calculated as one minus the probability that neither die shows four points: P(at least one die shows four points) = = 1 - P(neither die shows four points) = 1 - P(first die does not show four points) * P(second die does not show four points) = 1 - (5/6) * (5/6) =11/36
If two events are independent, then the probability that both events occur simultaneously can be calculated as the product of their probabilities: P(both machines need to be regulated within an hour) = = P(first machine needs to be regulated within an hour) * P(second machine needs to be regulated within an hour) =0.8 *0.7 =0.56
15.The area of a circle is proportional to the square of its radius so if we consider each ring as a target then their areas will be proportional to R^2 and (4R)^2 respectively. The ratio between these areas will be R^2 : (4R)^2 = R^2 :16R^2 =1:16 So if we consider each unit area as having an equal chance to be hit then we have: P(the shot hit the smaller ring)= Area(smaller ring)/(Area(smaller ring)+Area(larger ring))=1/(16+1)=1/17
16.There are four winning tickets out of twenty tickets in total in a lottery so if Ilze buys one ticket then her chance to get a winning ticket will be: P(Ilze’s ticket is a winning ticket)= Number of winning tickets / Total number of tickets=4/20=1/5
17.The day on which someone was born can be any day from Monday to Sunday with equal chances so if we consider two friends then: P(both friends were born on Saturday)=P(first friend was born on Saturday)P(second friend was born on Saturday)=(1/7)(1/7)=1/49
18.The student knows seven out of eight questions so if two questions are included in a test then his chance to know both questions will be: P(the student knows both questions)= Number of ways to choose two known questions / Number of ways to choose any two questions=(7 choose 2)/(8 choose 2)=21/28=3/4
19.There are four cards labeled with letters A,P,S,E so if three cards are drawn successively without replacement then there will be: Number of ways to draw three cards=Number of ways to draw first cardNumber of ways to draw second cardNumber of ways to draw third card=432=24 The only way for these cards to be drawn in order A,P,E will be if they are drawn successively as A,P,E so: P(the cards are drawn in order A,P,E)=Number of ways for cards to be drawn in order A,P,E / Number of ways for any three cards to be drawn=1/24
20.Two dice have six faces each so when they are rolled simultaneously there will be: Number of possible outcomes=Number of faces on first dieNumber of faces on second die=66=36 None of these outcomes will result in a sum equal to fourteen so: P(the sum of numbers rolled equals fourteen)=0