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.

a.

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

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

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

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

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

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

b.

c.

Events V and F are not mutually exclusive

Step-by-step explanation:

Given

Solving (a): Outcomes and Probabilities

The text is made of the following makeup.

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

So:

In tabular form, we have:

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

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

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

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

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

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

Solving (b)

Calculating P(V)

P(V) = Number of vowels divided by total

The vowels are A and I.

So, number of vowels is 2

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:

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

22 dimes and 9 nickels

step-by-step explanation: