Question

A candy store has ten giant pieces of candy! Find the probability of each event. There are 4 gumdrops, 3 lolipops, 2 jellybeans, and 1 peppermint. 1. What is the probability that a child will pick a peppermint or a jellybean, then a lollipop? 2. What is the probability that a child will pick a lollipop or peppermint, then a gumdrop? 3. What is the probability that a child will pick a jellybean, then a peppermint or a gumdrop? 4. What is the probability that a child will pick a peppermint, then a gumdrop?

Answer 1

Answer:

1. P = 9/90 = 1/10

2. P = 16/90 = 8/45

3. P = 10/90 = 1/9

4. P = 4/90 = 2/45

Step-by-step explanation:

Total no. of candy = 10

No. of Gumdrops = 4

No. of Lollipops = 3

No. of Jellybeans = 2

No. of Peppermint = 1

1. To find the probability that the child will pick a peppermint or jellybean, we will add the probabilities of both the candies.

P(Peppermint) = No. of Peppermint/Total no. of candy

                        = 1/10

P(Jellybean) = No. of Jellybean/Total no. of candy

                    = 2/10

P(Peppermint or Jellybean) = 1/10 + 2/10

P(Peppermint or Jellybean) = 3/10

Then, the child picks a lollipop. Note that after picking a peppermint or a jellybean, the number of candies left are 9. So,

P(Lollipop) = No. of Lollipops/Total no. of candy

P(Lollipop) = 3/9

To compute the probability that the child will pick a peppermint or a jellybean and then a lollipop,

P = P(Peppermint or Jellybean) x P(Lollipop)

  = 3/10 x 3/9

P = 9/90 = 1/10

2. Probability that a child will pick a lollipop or peppermint:

P(Lollipop or Peppermint) = P(lollipop) + P(peppermint)

                                          = 3/10 + 1/10

P(Lollipop or Peppermint) = 4/10

Then the child picks a gumdrop. Note that the number of candies remaining are 9. So,

P(Gumdrop) = 4/9

The probability that the child picks a lollipop or peppermint and then a gumdrop:

P = P(Lollipop or Peppermint) x P(Gumdrop)

  = 4/10 x 4/9

P = 16/90 = 8/45

3. Probability that a child will pick a jellybean:

P(Jellybean) = No. of Jellybeans/Total no. of candy

P(Jellybean) = 2/10

Then the child picks a peppermint or a gumdrop. Note that one candy has been picked out so there are 9 candies left in total.

P(Peppermint or Gumdrop) = P(peppermint) + P(Gumdrop)

                                              = 1/9 + 4/9

P(Peppermint or Gumdrop) = 5/9

The probability that a child picks a jellybean then a peppermint or a gumdrop is:

P = P(Jellybean) x P(Peppermint or Gumdrop)

  = 2/10 x 5/9

P = 10/90 = 1/9

4. P(peppermint) = 1/10

Then the child picks a gumdrop. (remaining candies are 9)

P(Gumdrop) = 4/9

Probability that a child will pick a peppermint then a gumdrop:

P = P(peppermint) x P(gumdrop)

  = 1/10 x 4/9

P = 4/90 = 2/45