One more probability question

[cait88]

3 girls, M, P and R will participate in a round-robin tennis tournament in which each one plays both of the other. The friends estimate that the probability that M beats P is 0.7, the probability that M beats R is 0.8 and the probability that P beats R is 0.6. Assume the outcomes of the three matches are independent.

a) What is the probability that M loses both her matches?
b) What is the probability that M wins both her matches and P beats R?
c) What is the probability that each person wins one match?

Any ideas which probability equations I am expected to use for these questions?

Thanks a lot

 

[Deleted member 4993]

3 girls, M, P and R will participate in a round-robin tennis tournament in which each one plays both of the other. The friends estimate that the probability that M beats P is 0.7, the probability that M beats R is 0.8 and the probability that P beats R is 0.6. Assume the outcomes of the three matches are independent.

a) What is the probability that M loses both her matches?
b) What is the probability that M wins both her matches and P beats R?
c) What is the probability that each person wins one match?

Any ideas which probability equations I am expected to use for these questions?

Thanks a lot

What are your thoughts?

 

[cait88]

P(M beats P) = 0.7 P(P beats M) = 0.3
P(M beats R) = 0.8 P(R beats M) = 0.2
P(P beats R) = 0.6 P(R beats P) = 0.4

So I just multiply each probability for each question?

For example:
a) What is the probability that M loses both her matches?

P(P beats M) = 0.3
P(R beats M) = 0.2

P(P beats M and R beats M) = (0.3)(0.2) = 0.06

 

[soroban]

Hello, cait88!

You're correct . . .

\(\displaystyle \begin{array}{ccccccc}
P(\text{M beats P}) & = & 0.7 & \;\;\;& P(\text{P beats M}) & = & 0.3 \\
P(\text{M beats R}) & = & 0.8 &\;\;\;& P(\text{R beats M}) & = & 0.2 \\
P(\text{P beats R}) & = & 0.6 &\;\;\;& P(\text{R beats P}) & = & 0.4\end{array}\;\;\) . . . Nice!

For example:
a) What is the probability that M loses both her matches?

\(\displaystyle P(\text{P beats M}) \:= \:0.3\)
\(\displaystyle P(\text{R beats M}) \:= \:0.2\)

\(\displaystyle P(\text{P beats M and R beats M}) \:=\: (0.3)(0.2)\: =\: 0.06\;\;\) . . . Right!

c) There are two ways in which each player wins one match.

. . \(\displaystyle P\bigg[(\text{M beats P) }\wedge \text{ (P beats R) }\wedge \text{ (R beats M)}\bigg] \;=\;(0.7)(0.6)(0.2) \;=\;0.084\)

. . \(\displaystyle P\bigg[\text{P beats M) }\wedge \text{ (M beats R) }\wedge\text{ (R beats P)}\bigg] \;=\;(0.3)(0.8)(0.4) \;=\;0.096\)

Therefore: \(\displaystyle \,P(\text{each wins one match}) \;=\;0.084\,+\,0.096\;=\;\L\fbox{0.18}\)