Question

Four vitamin and five sugar tablets identical in appearance are in a box. Those are the only things in the box. One tablet is taken at random and given to Person A. Without replacing it, a second tablet is then selected and given to Person B. What is the probability that

- Person B was given a sugar tablet given that Person A was given a vitamin tablet?

- neither was given vitamin tablets? -both were given vitamin tablets?

-Person A was given a sugar tablet and Person B was given a vitamin tablet?

-Person A was given a vitamin tablet and Person B was given a sugar tablet?

-exactly one person was given a vitamin tablet?

Answer 1

Given that there are 4 Vitamin and 5 Sugar tablets in a box. Out of total 9 tablets in a box one tablet is selected at random and given to person A (without replacement), and then second tablet is selected and given to person B.

Total number of tablets in the box = 4 + 5 = 9 tablets.

(a). P (that person B was given a sugar tablet given person A was given vitamin tablet)

Number of favorable outcomes for sugar tablets =

As it is given that 1 vitamin tablet is already given to person A. So, total number of tablets remaining in the box = 9 – 1 = 8 tablets.

Now for total outcomes that person B gets the second tablet =

So, required probability is

(b). P (neither was given vitamin tablets)

If both persons were given sugar tablets then,

(c). P (both were given vitamin tablets)

(d). P (person A was given sugar tablet and person B was given vitamin tablet)

(e). P (person A was given a vitamin tablet and person B was given a sugar tablet)

(f). P (exactly one person was given vitamin tablets)

1 – [P (neither were given vitamin tablet) – P (both were given vitamin tablets)]