Question

a computer user tries to recall her password .she knows it can be one of 4 possible passowrds.she tries her password until she finds the right one .let X be the number of wrong passwords she uses before she finds the right one.find E(x)

Answer 1

For the expected value, for each outcome, multiply that outcome with the probability of getting that outcome. Add up all of those values and that is the expected value.

For this, outcome 0 has probability 1/4. Outcome 1 has probability 3/4 * 1/3 (since on second attempt you can probability assume she doesn't try the same password she just got wrong). Outcome 2 has probability 3/4*2/3*1/2. Outcome 3 has probability 3/4*2/3*1/2.

The expected value is therefore: 0*1/4 + 1*3/4*1/3 + 2 * 3/4*2/3*1/2 + 3 * 3/4*2/3*1/2.

Answer 2

That comes out as 1.5.

Answer 3

thank u .i got it