Exercise: More on Probability

  1. A bowl on a dinner table has 10 black olives and 6 green olives. Jaime stands eats an olive after picking an olive at random from the bowl. He then picks another olive at random and eats the second olive.
    1. Draw a tree diagram to represents all the possible outcomes of these two picks by Jaime.

      Use your tree diagram or otherwise and find the probability
    2. that Jaime eats a black olive and a green olive.
    3. that Jaime eats a black olive first and then a green olive.
    4. that Jaime eats two olives of the same colour.

  2. Edwin was offered a plate with 10 marshmallows, 3 of them were green, 2 blue and 5 red. He picked and ate two marshmallows at random one after the other.
    1. Draw a tree diagram to represents all the possible outcomes of these two picks made by Edwin.

      Use your tree diagram or otherwise and find the probability
    2. that Edwin ate a red marshmallow and a green marshmallow.
    3. that Edwin ate two marshmallows of the same colour.

  3. Santa has 10 chocolate bars and 35 granola bars in his bag. Nirvan and Junius are asked to pick an item at random from Santa's bag. Find the probability that
    1. Junius picks a chocolate bar if he picks before Nirvan.
    2. Junius picks a granola bar if he picks after Nirvan.
    3. both Junius and Nirvan pick the same type of snack regardless of who picks first.

  4. In a cafetaria, each student standing in a line (queue) will be given a fruit that is picked at random from a basket that has 5 peaches, 4 apples and 6 nectarines. Find the probability that
    1. the first three people in the line will receive a peach each
    2. the first three people all will receive different fruits.
    3. the second person in the line will receive a peach
    Hint: Draw a tree diagram.

  5. Albert, Bertha, Cindy, Devi, Enrique, and Fu-Yu are members of Model United Nations. Two students will be selected from this group to attend a conference in Geneva.
    1. With the aid of an appropriate diagram (hints: table of outcomes), find the number of different possible combinations of two students that could attend the conference.
    2. Find the probability that Devi will be selected for the conference.
    3. Find the probability that Devi and Enrique will be selected for the conference

  6. A class has 50 student and each student either plays or not play the violin.
    1. Complete the table below.
        plays violin does not play violin Total
      Male 16 10  
      Female   12  
      Total     50
    2. A student is selected at random to represent the class in a music conference. Find the probability that the student is a female and plays violin.
    3. Two students are now selected at random to represent the class. What is the probability that both students are female or both students play violin?

Solutions