Question

A box contains 6 letters, shown as CARTED What is the probability of the out come RAT in that order if 3 letters are drawn one by one​

(a) with​ replacement?

(b) without​ replacement?

The probability of the outcome RAT in that order if 3 letters are drawn with replacement is ?

Answer 1

a) Given that we are drawing with replacement, the probability that we get RAT in that same order is computed here as:

= (1/6)*(1/6)*(1/6)

= 1/216

as each draw has equal probability of getting any of the 6 letters

Therefore 1/216 is the required probability here.

b) Now given that we are drawing the letters without replacement, probability that we get the required letters in that order is computed here as:

= Probability of getting R in first draw * Probability of getting A in second draw given that we are left with 5 letters * Probability of getting T in third draw given that 4 letters are left

= (1/6)*(1/5)*(1/4)

= 1/120

Therefore 1/120 is the required probability here.