Respuesta :
Answer:
a) See attachment
b) P ( exactly one six ) = 0.0256
Step-by-step explanation:
Solution:-
- To develop a probability tree diagram for rolling a biased die 2 times.
- The probability of getting a 6 on each roll is constant and independent between the trials ( rolls ).
- We will consider 2 general probability:
Probability of getting a 6, p = 1/5
Probability of not getting a 6, q = 4/5
- For the first roll there are two branches. ( p and q )
- The second roll will entail sub branches for each outcome in first roll.
So, after rolling a 6. We again have two possibilities of either rolling another 6 or not getting a 6.
OR
So, after rolling any number other than 6. We again have two possibilities of either rolling a 6 or not getting a 6.
- So, the second roll will have a total of 4 possibilities with the probability of each outcome remains constant and independent from each roll.
The tree diagram is given as an attachment.
B)
- Once we have developed a tree diagram. We will use it to determine the probability of getting exactly one six out of two rolls.
- First we determine the "paths" that have only one 6. We have 2 paths as follows:
Path 1: ( First throw = 6 , Second throw = Not getting a 6 )
Path 2: ( First throw = Not getting a 6 , Second throw = 6 )
- Now we will determine the probabilities for each path.
Note: Remember that while using a tree diagram we multiply all the probabilities along the same path and sum the resultant probabilities of different paths.
Path 1:
P ( Getting a 6 )*P ( Not getting a 6 )
p*q
( 1 / 5 )*( 4 / 5 )
= ( 4 / 25 )
Path 2:
P ( Not getting a 6 )*P ( 6 )
q*p
( 4 / 5 )*( 1 / 5 )
= ( 4 / 25 )
- Now add the probabilities of different paths to determine the probability of getting exactly one 6.
P ( Exactly one 6 ) = Path 1 + Path 2
= ( 4 / 25 ) + ( 4 / 25 )
= ( 16 / 625 )
= 0.0256 ( answer )
