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Answer:
The probability of Thomas inviting Madeline to the party over the phone is 0.143.
Step-by-step explanation:
Consider the tree diagram below.
The events are denoted as follows:
<em>A</em> = Thomas bumps into Madeline at school
<em>B</em> = Thomas call Madeline on the phone
<em>X</em> = Thomas asks Madeline to the party
The information provided is:
P (A) = 0.80
P (B) = 1 - P (A) = 1 - 0.80 = 0.20
P (X|A) = 0.90
⇒ P (X'|A) = 1 - P (X|A) = 1 - 0.90 = 0.10
P (X|B) = 0.60
⇒ P (X'|B) = 1 - P (X|B) = 1 - 0.60 = 0.40
The conditional probability of event <em>U</em> given that another events <em>V</em> has already occurred is:
The law of total probability states that:
In this case we need to determine the probability that Thomas invites Madeline to the party over the phone, i.e. P (B|X).
Use the law of total probability to determine the value of P (X) as follows:
Compute the value of P (B|X) as follows:
Thus, the probability of Thomas inviting Madeline to the party over the phone is 0.143.