1A coin is tossed three times. Draw a probability tree diagram to show all the possible outcomes. Then find the probability that all three are tails, the probability of at least two heads, and the probability of three tails.
2A spinner with three colours, red, blue and brown, is spun and a coin is tossed together. Draw a probability tree diagram to show all the possible outcomes. Use it to find the probability that the spinner lands on red and the coin shows head, and the probability that the spinner lands on brown and the coin shows tail or head.
3A coin is tossed and a die is rolled one after another. Draw a probability tree diagram to show all the possible outcomes. Use it to find the probability of a head on the coin and an even number on the die, and the probability of a tail on the coin and a square number on the die.
4A card is drawn from a well-shuffled pack of 52 cards and its suit (spade, club, diamond or heart) is noted, and a coin is tossed. Draw a probability tree diagram to show all the possible outcomes. Use it to find the probability of a red card and a head on the coin, and of a black card and a tail on the coin.
5A bag contains 7 red and 5 green marbles. Three marbles are drawn one after another, first with replacement and then without replacement. Draw a probability tree diagram to show all the possible outcomes in each case.
6Project work: three cards are drawn one after another at random from a deck of 52 cards without replacement. Draw a probability diagram and find the probability that all three cards are spades, that only two are spades, that only one is a spade, and that none of them is a spade.
7The heights (in cm) of 50 people are: 125, 137, 155, 149, 122, 128, 133, 144, 115, 118, 142, 145, 151, 157, 159, 160, 165, 162, 156, 158, 155, 141, 147, 149, 148, 159, 154, 155, 166, 168, 169, 172, 174, 173, 176, 161, 164, 163, 149, 150, 154, 153, 152, 164, 158, 159, 162, 157, 156, 155. Construct a frequency distribution table with class interval 10, find the mean from it, show its histogram, and find the median.
8The weights (in kg) of 63 students of a school are: 18, 20, 13, 24, 35, 34, 56, 45, 33, 23, 24, 56, 33, 22, 26, 35, 39, 44, 42, 47, 46, 48, 55, 51, 44, 40, 47, 49, 34, 31, 28, 29, 35, 39, 28, 48, 51, 50, 47, 23, 19, 27, 57, 42, 33, 23, 38, 36, 45, 45, 37, 29, 27, 22, 28, 36, 35, 57, 54, 40, 50, 30, 29. Construct a frequency distribution table with class interval 5, prepare less than and more than cumulative frequency tables, and find the difference between the mode and the median.
9In a community survey of job holders' ages, 0-15 years had 5 persons, 15-30 had 6, 30-45 had 10, 45-60 had 6 and 60-75 had 3. Which age group has the most employees? What is the average age? Angel said that the mean and the median lie in the same class interval. Is she right?
10The monthly electricity consumption of 40 households of Thaha Municipality is: 10-20 units, 5 households; 20-30, 6; 30-40, 8; 40-50, 9; 50-60, 7; 60-70, 4; 70-80, 1. Prepare less than and more than cumulative frequency tables, draw the cumulative frequency curves, and say whether the mean and median lie in the same class interval.
11The ages of patients admitted to a hospital in a week are: 0-10 years, 4; 10-20, 5; 20-30, 8; 30-40, 13; 40-50, 12; 50-60, 8; 60-70, 4; 70-80, 9; 80-90, 7. Find the first and third quartiles and the value that divides the patients into two equal parts. Niruta said that the mode and median lie in the same class interval. Is she correct?
12The monthly expenditure (in thousands) of the families of Lamapatan is: 10-20, 3 families; 20-30, 2; 30-40, 6; 40-50, 5; 50-60, 4. Write the modal class, find the expenditure of the largest number of families (the mode), and find the first and third quartiles.
13The mathematics marks of class 10 students in the second terminal examination are: 0-5, 2 students; 5-10, 4; 10-15, 5; 15-20, 3; 20-25, 2; 25-30, 4. How many students obtained less than 20? Construct the cumulative frequency table. Find the values that divide the data into 4 equal parts. Based on the median, how many students at most obtained marks less than the median?
14Three coins are tossed together. Write the possible outcomes, and find the probability of getting only one head, of getting at least two tails, of getting no head, and of getting two heads or no head.
15A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of getting an ace, a spade or a diamond, a spade or an ace, and a club or a face card.
16A coin is tossed and a spinner with 4 colours (blue, green, red, purple) is spun together. Draw a probability tree diagram and write the possible outcomes separately and together. Find the probability of a head on the coin with the needle on green or blue, and of a head with the needle on green.
17Two cards are drawn at random one after another from a well-shuffled deck of 52 cards. If the first card is replaced before the second is drawn, what is the probability that both are spades? If it is not replaced, what is the probability that the first is a spade and the second a heart? Show a probability tree diagram for each case.
18A bag contains 7 red and 8 yellow balls of the same shape and size. If two balls are drawn one after another without replacement, find the probability that both are red. If they are drawn with replacement, find the probability that both are red. Ramila said that both situations are independent. Is she correct?
19A bag contains one red, one green and one black ball of the same shape and size. One ball is drawn at random and, without replacing it, another ball is drawn. Show the probability tree diagram and find the probability of each outcome.
20A coin is tossed and a die is thrown. Draw a probability tree diagram. Use it to find the probability of a head and an even number, and of a tail and a square number. Are these events independent? Give a reason.
21A card is drawn at random from a well-shuffled deck of 52 cards (spade, club, diamond and heart) and a coin is tossed. Draw the probability tree diagram and write the sample space. Find the probability of a red card and a head, and of a black card and a tail. Bikash said that the events from the card and the coin are dependent. Is he correct?
22A bag contains 7 red and 5 green marbles. Two marbles are drawn at random one after another, once with replacement and once without replacement. Draw a probability tree diagram for each case. Find the probability that both marbles are red and that both are green. Without replacement, is the probability of red first and green second equal to the probability of green first and red second?
23A card is drawn at random from number cards 1 to 20. List the cards divisible by 3 and those divisible by 5. Find the probability of a card divisible only by 3 or only by 5. Kopila said that the two events are not mutually exclusive. Is she correct? Find the probability of a card divisible by 3 or by 5.
24A bag has 5 red and 3 blue balls. A ball is drawn at random and replaced before the second ball is drawn. Find the probability that both balls are blue and the probability that neither is blue, and show both in a tree diagram.
25A bag has 4 red and 6 blue balls. Two balls are drawn without replacement. Use a tree diagram to find the probability that the two balls are of different colours.
26Two branches leave one point of a tree diagram. One of them is marked 0.3. What must the other be, and why?
27Why is the probability of 'one blue and one white' found by adding two paths, while 'white first and green second' uses only one path?