Answer:
0.78 or 78 % probability that Barcelona will win their next match
Step-by-step explanation:
To find the probability that Barcelona wins their next match, we can use the law of total probability. Let's break it down step by step:
Let W represent the event that Barcelona wins
M represent the event that Messi plays
M' represent the event that Messi does not play
Using these the probabilities are:
P(W|M) = 0.8 → Probability that Barcelona wins when Messi plays P(W|M') = 0.6 → Probability that Barcelona wins when Messi doesn't play
P(M) = 0.9 → Probability that Messi plays)
We need to find P(W) the probability that Barcelona wins their next match.
P(W) = P(W|M) · P(M) + P(W|M') · P(M')
Calculate the probability that Messi doesn't play:
P(M') = 1 - P(M) = 1 - 0.9 = 0.1
Substitute the values into the formula:
P(W) = 0.8 x 0.9 + 0.6 x 0.1
P(W)= 0.72 + 0.06
P(W) = 0.78
Therefore, the probability that Barcelona wins their next match is 0.78 or 78%.
