Probability-Sample Papers

CLASS IX MATH
TEST FOR PROBABILITY
TIME : 60 MIN
MARKS : 26
Q. 1 � 4 are of two marks each.
Q. 5 � 10 are of three marks each.
1.  Eleven bags of wheat flour, each marked 5 kg actually contained the following weights of flour (in kg):
            4.97      5.05      5.08      5.03      5.00      5.06      5.08      4.98      5.04      5.07      5.00
      Find the probability that any of these bags chosen at random contains more than 5 kg of flour.
2.  Given below is the frequency distribution table regarding the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city for 30 days:
      Conc. of SO2: 0.00-0.04 0.04-0.08 0.08-0.12 0.12-0.16 0.16-0.20 0.20-0.24
      No. of days : 4 8 9 2 4 3
      Find the probability of concentration of sulphur dioxide in the interval (0.12 – 0.16) on any of these days.
3.  Answer the following:
      (i) If P(E) = 0.2, find P (not E).
      (ii) “Probability of an event cannot be greater than 1”. Is the statement true or false?
      (iii) What is the probability of a sure event?
      (iv) If a coin is tossed 40 times and 19 times head appears and 21 times tail appears, write the probability of getting a head in a trial out of these 40 trials of the experiment.
4.  A type manufacturing company kept a record of the distance covered before a tyre needed to be replaced. The table show the result of 1000 cases:
      Distance (in km) Less than 4000 4000 to 9000 9000 to 14000 More than 14000
      Frequency 20 210 325 445
      If a tyre of this company is bought, what is the probability that:
      (i) it will need to be replaced before it has covered 4000 km?
      (ii) it will last more than 9000 km?
      (iii) it will need to be replaced after it has covered between 4000 km and 14000 km?
5.  A survey was conducted by car manufacturing company in a metropolitan city on 1000 persons having monthly income from Rs. 30,001 to Rs. 50000. The data about the number of persons in various categories is as under.
      Find the probability that a person selected at random
      (i) in the income slab 40,001 – 50,000 have more than 2 cars.
      (ii) in the income slab 30,001 to 50,000 have two cars.
6.  Twenty bags of sugar, each marked 10 kg, actually give the following data:
   Weight of a bag (in kg) 9.5 � 9.8 9.8 � 9.9 9.9 � 10.0 10.0 � 10.1
   Number of bags 1 2 5 12
      What is the probability that the bag selected at random weigh 10 kg or more?
7.  A die having six faces is tossed 80 times and the data is as below:
   Outcome 1 2 3 4 5 6
   Frequency 10 20 10 28 8 4
      Find (i) P (1)      (ii) P (4)      (iii) P (6)      (iv) P (5).
8.  The blood groups of 30 students of class IX are recorded as follows:
      A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O,
      A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O
      A student is selected at random from the class from blood donation. Find the probability that the blood groups of the student chosen is:
      (i) A      (ii) B      (iii) AB      (iv) O
9.  The following table gives the lifetime of 400 lamps:
      Lifetime
(in hrs)		 300�400 400�500 500�600 600�700 700�800 800�900 900�1000
      No. of
lamps		 14 56 60 86 74 62 48
      A bulb is selected at random. Find the probability that the life time of the selected bulb is:
      (i) less than 400 hours
      (ii) between 300 to 800 hours
      (iii) at least 700 hours
10.  Given below is the frequency distribution of wages (in Rs.) of 30 workers in a certain factory
      Wages
(in Rs.)		 110-130 130-150 150-170 170-190 190-210 210-230 230-250
      No. of
workers		 3 4 5 6 5 4 3
      A worker is selected at random. Find the probability that his wages are:
      (i) less than Rs. 150
      (ii) at least Rs. 210
      (iii) more than or equal to 150 but less than 210.