Question

A bag contains 3 purple and 5 orange jelly-beans. If one jelly-bean is selected and is NOT replaced and a second jelly-bean is selected, find P(orange and then a purple) *

A bag contains 3 purple and 5 orange jelly-beans. If one jelly-bean is selected and is NOT replaced and a second jelly-bean is selected, find P(two purples in a row) *

Answer 1

P(orange and then a purple) is 15/56.

P(two purples in a row) is 6/56.

Explanation:

• A bag contains 3 purple and 5 orange jelly-beans.
• The total jelly-beans in the bag = 3 purple + 5 orange = 8 jelly-beans.

Without replacement, find P(orange and then a purple) :

P (orange) = No.of orange jelly-beans / total jelly-beans.

⇒ 5 / 8

P (purple) = No.of purple jelly-beans / remaining jelly-beans from the total

⇒ 3 / 7

P(orange and then a purple) = P (orange) × P (purple)

⇒ 5/8 × 3/7

⇒ 15/56

Without replacement, find P(two purples in a row) :

P (1st purple) = No.of purple jelly-beans / total jelly-beans.

⇒ 3 / 8

P (2nd purple) = remaining no.of purple jelly-beans / remaining jelly-beans from the total.

⇒ 2 / 7

P(two purples in a row) = P (1st purple) × P (2nd purple)

⇒ 3/8 × 2/7

⇒ 6/56