Question

A bag contains 20 slips of paper Individually numbered. If a slip of paper and a letter in the word PENNSYLVANIA is chosen at randomfind each probability.

Answer 1

`P(M4\ n\ V) = 2.083\%`

Explanation:

Given

Paper = 20 slips

Word: PENNSYLVANIA

Required

Determine P(Multiple of 4 and V)

The sample size of the 20 slips is:

`n(S) = 20`

The outcomes of multiples of 4 is:

`M4= \{4,8,12,16,20\}`

`n(M4) = 5`

So, the probability of multiples of 4 is:

`Pr(M4) = (5)/(20)`

`Pr(M4) = (1)/(4)`

The sample size of PENNSYLVANIA is:

`n(S) = 12`

The outcome of V is:

`n(V) = 1`

So, the probability of V is:

`P(V) = (1)/(12)`

So, the required probability is: P(Multiple of 4 and V)

`P(M4\ n\ V) = P(M4) * P(V)`

`P(M4\ n\ V) = (1)/(4) * (1)/(12)`

`P(M4\ n\ V) = (1)/(48)`

`P(M4\ n\ V) = 0.02083`

Express as percentage

`P(M4\ n\ V) = 0.02083 * 100\%`

`P(M4\ n\ V) = 2.083\%`