Correct Answer - Option 2 : 14/33
Given:
In a basket, there are 4 orange balloons and 8 yellow balloons
Concept used:
The classical definition of probability.
Formula used:
Probability = Favorable Outcome/Total Outcome.
P(E) = n(E)/n(S)
nCr = n!/r!(n-r)!
n! = n × (n - 1) × (n - 2) × ... × 3 × 2 × 1
Calculation:
Number of favorable outcomes,
n(E) = number of ways 2 yellow balloons can be selected from 8 yellow balloons
⇒ 8C2 = 8!/{2! × (8 - 2)!} = 28
Total number of possible outcomes
n(S) = number of ways 2 balloons can be selected from 12 balloons
⇒ 12C2 = 12!/{2! × (12 - 2)!} = 66
P(E) = n(E)/n(S)
⇒ 28/66
⇒ 14/33
∴ The probability that 2 first balloons are yellow is 14/33.