Question

The letters in the word STATISTICS are printed on identical index cards with one letter per card. The ten cards are
then placed in a hat, and one card is randomly chosen (without looking) from the hat. The random process we are
interested in is what letter is on the selected card.
(a) Make a table that shows the set of outcomes and the probability of each outcome.
Outcome
Probability
(b) Consider the following events:
V: the letter chosen is a vowel.
F: the letter chosen falls in the first half of the alphabet (that is, between A and M).
Determine the following probabilities:
P(V) =

P(F) =
P(FC
) =

P(V and F) =

P(V or F) =

(c) Are the events V and F mutually exclusive (disjoint)? Explain.

Answer 1

Answer:

a.

Outcome ---------- Probability

S -------------------------- 0.3

T -------------------------- 0.3

A -------------------------- 0.1

I --------------------------- 0.2

S -------------------------- 0.1

b.

$P(V) = 2/10$

$P(F) = 2/10$

c.

Events V and F are not mutually exclusive

Step-by-step explanation:

Given

$Text: STATISTICS$

Solving (a): Outcomes and Probabilities

The text is made of the following makeup.

$S = 3$

$T = 3$

$A = 1$

$I = 2$

$C = 1$

$Total = 10$

The probability of each outcome is calculated by dividing the occurrence of each alphabet by the total number of alphabets

So:

$S = 3/10 = 0.3$

$T = 3/10 = 0.3$

$A = 1/10 = 0.1$

$I = 2/10 = 0.2$

$C = 1/10 = 0.1$

In tabular form, we have:

Outcome ---------- Probability

S -------------------------- 0.3

T -------------------------- 0.3

A -------------------------- 0.1

I --------------------------- 0.2

S -------------------------- 0.1

Solving (b)

$V = Vowels$

$F = A - M$

Calculating P(V)

P(V) = Number of vowels divided by total

The vowels are A and I.

So, number of vowels is 2

$P(V) = 2/10$

Calculating P(F)

P(F) = Number of alphabets from A to M divided by total

Alphabets from A and M are A and I

So, number of alphabets in this category is 2

So:

$P(F) = 2/10$

Solving (c):

Events V and F are not mutually exclusive because both can occur at the same time.

i.e.

An event can be a vowel and still be between A and M