Probability topic

Question

3 cards are drawn at random successively with replacement from well shuffled cards .getting a card of "diamond is treated as success ".what is the sum of Probability of which random variable 'x' will be x>=2.

 

(a)5/32

(b)6/32

(c)8/45

(d)9/32

Answer 1

I assume that the variable x represents the number of successes?

 

There are 4 ways that the number of successes can be ≥ 2:

 

SSS

SSF

SFS

FSS

 

...where S represents success and F represents failure.

 

Since the probability of S on each draw is 1/4, the probability of failure is 3/4.  We can then calculate the probability of each of these combinations:

 

SSS -- 1/4 * 1/4 * 1/4 = 1/64

SSF -- 1/4 * 1/4 * 3/4 = 3/64

SFS -- 1/4 * 3/4 * 1/4 = 3/64

FSS -- 3/4 * 1/4 * 1/4 = 3/64

 

Adding the probabilities together, we get 10/64 = 5/32.  So the answer is (a).