Correct Answer - Option 3 : 7/102
Given:
A container contains 6 white, 8 blue and 4 red marbles. Three marbles are drawn at random from the container
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)!
nCr = nC(n - r)
Calculation:
Total number of marbles is 6 + 8 + 4 = 18
Let S be the sample space
n(S) = Total number of ways of drawing 3 marbles out of 18 = 18C3
Let E = Event of drawing 3 marbles, all of them are blue
n(E) = Number of ways of drawing 3 marbles, all of them are blue
Number of ways of drawing 3 marbles from the total 8 = 8C3
P(E) = n(E) / n(S)
⇒ 8C3/18C3
⇒ {(8 × 7 × 6)/(1 × 2 × 3)}/{(18 × 17 × 16)/(1 × 2 × 3)}
⇒ 56/816
⇒ 7/102
∴ The probability that all of them are blue is 7/102.