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
