Question

A basket contains 10 red rose and 15 yellow rose. Out of which 3 red and 4 yellow roses are dried. If two roses
selected at random, what is the probability that either both are yellow roses or both are not dried?​

Answer 1

Given :- A basket contains 10 red rose and 15 yellow rose. Out of which 3 red and 4 yellow roses are dried.

To Find :- If two roses selected at random, what is the probability that either both are yellow roses or both are not dried ?

Answer :-

Let us assume that,

• P(Y) = Probability of getting both yellow roses .
• P(N) = Probability of getting both are not dried .
• P(Y ∩ N) = Probability of getting both yellow not dried .

so,

→ P(Y) = 15(C)2 / 25(C)2 = [15! / 13! * 2!] / [25! / (23! * 2!)] = (15 * 14/2) / (25 * 24/2) = (15 * 7) / (25 * 12) = (7/20)

and,

→ P(N) = 18(C)2 / 25(C)2 = [18! / 16! * 2!] / [25! / (23! * 2!)] = (18 * 17/2) / (25 * 24/2) = (9 * 17) / (25 * 12) = (51/100)

also,

→ P(Y ∩ N) = 11(C)2 / 25(C)2 = [11! / 9! * 2!] / [25! / (23! * 2!)] = (11 * 10/2) / (25 * 24/2) = (11 * 5) / (25 * 12) = (11/60)

then,

→ P(Y ∪ N) = P(Y) + P(N) - P(Y ∩ N)

→ P(Y ∪ N) = (7/20) + (51/100) - (11/60)

→ P(Y ∪ N) = (15*7 + 51*3 - 11*5)/300

→ P(Y ∪ N) = (105 + 153 - 55)/300

→ P(Y ∪ N) = (258 - 55)/300

→ P(Y ∪ N) = (203/300) (Ans.)

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