Question

A briefcase contains 11 black beads and 9 burgundy beads. If Ananya picks one bead without replacing it back to the briefcase, and then picks another bead, what is the probability that Ananya gets at least one burgundy bead?

Answer 1

Probability (at least 1 burgundy bead) =
`(270)/(380)`

Explanation:

Briefcase contains: 11 black beads; 9 burgundy beads

According to the question,

Ananya picked 2 beads without replacement;

Probability (at least 1 burgundy beads) = probability (1 burgundy beads) + probability (2 burgundy beads)

Now, we know that for any event,

probability (occurrence of event) + probability (non occurrence of event) = 1

so, the above case can also be rewritten as

Probability (at least 1 burgundy beads)= 1 - probability (no burgundy beads)

Probability (at least 1 burgundy beads)= 1 - probability (both black beads)

Probability (at least 1 burgundy beads) = 1 - probability (black, black)

Probability (at least 1 burgundy beads) = 1 - (
`(11)/(20) * (10)/(19)`)

Probability (at least 1 burgundy beads) = 1 -
`(110)/(380)`

Probability (at least 1 burgundy beads) =
`(380-110)/(380)`

Probability (at least 1 burgundy beads) =
`(270)/(380)`