With probability !
1) the graph shows the number of each kind of book in hero's personal library. a book is chosen randomly. what is the probability that the book chosen is a science fiction book?
a)1/30
b)14/15
c)7/15
d)1/4
2)marlene is a tennis player who has won 55% of her tennis matches. what is the probability that she will lose her next tennis match?
a) 55%
b)50%
c)45%
d)5%
3) six tiles lettered b, a,n, a,n and a are lying face down on a table . a tile is selected, the letter is recorded, the tile is replaced, and the process is repeated. what is the theoretical probability of selecting the letter a
a) 1/3
b)2/5
c)1/6
d)1/2

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.

The size of the sample space is the total number of possible outcomes

The event space is the number of outcomes in the event you are interested in.

so

The probability is the size of the event space divided by the size of the sample space

Part 1) What is the probability that the book chosen is a science fiction book?

Let

x--------> the size of the event space

y-------> the size of the sample space

P------> probability

in this problem we have

substitute

Simplify

therefore

the answer part 1) is the option C

Part 2) Marlene is a tennis player who has won of her tennis matches. What is the probability that she will lose her next tennis match?

we know that

the probability that she won is

so

the probability that she will lose is

therefore

the answer Part 2) is the option C

Part 3) Six tiles lettered B,A,N,A,N and A are lying face down on a table . A tile is selected, the letter is recorded, the tile is replaced, and the process is repeated. What is the theoretical probability of selecting the letter A

Let

x--------> the size of the event space

y-------> the size of the sample space

P------> probability

in this problem we have

substitute

Simplify

therefore

the answer Part 3) is the option D

the image of (6, 9) under a dilation is (4, 6). the scale factor is