The knock-out match is the one which emerges with a winner, no draw match. The football experts predict the outcome of two knock-out matches. The first match is of Simba against Ya... The knock-out match is the one which emerges with a winner, no draw match. The football experts predict the outcome of two knock-out matches. The first match is of Simba against Yanga, the second is of Real Madrid against Barcelona. The chance of Simba to win is 0.74 while that of Real Madrid to win is 0.65. What is the probability that both Yanga and Barcelona will win their matches?
Understand the Problem
The question describes two independent knockout football matches and gives the probability of Simba and Real Madrid winning their respective matches. It asks for the probability that both Yanga and Barcelona will win their respective matches. This requires calculating the probability of Yanga winning given the probability of Simba winning, and the probability of Barcelona winning given the probability of Real Madrid winning, and then multiplying the probabilities of Yanga and Barcelona winning.
Answer
$0.091$
Answer for screen readers
The probability that both Yanga and Barcelona will win their matches is $0.091$.
Steps to Solve
- Find the probability of Yanga winning
Since there is no draw in a knock-out match, the probability of Yanga winning is the complement of the probability of Simba winning. $P(\text{Yanga wins}) = 1 - P(\text{Simba wins})$ $P(\text{Yanga wins}) = 1 - 0.74 = 0.26$
- Find the probability of Barcelona winning
Likewise, the probability of Barcelona winning is the complement of the probability of Real Madrid winning. $P(\text{Barcelona wins}) = 1 - P(\text{Real Madrid wins})$ $P(\text{Barcelona wins}) = 1 - 0.65 = 0.35$
- Find the probability of both Yanga and Barcelona winning
Since the two matches are independent, we multiply the probabilities of each team winning. $P(\text{Yanga and Barcelona win}) = P(\text{Yanga wins}) \times P(\text{Barcelona wins})$ $P(\text{Yanga and Barcelona win}) = 0.26 \times 0.35 = 0.091$
The probability that both Yanga and Barcelona will win their matches is $0.091$.
More Information
The probability is a number between 0 and 1, representing the likelihood of an event occuring, where 0 means impossible and 1 means certain.
Tips
A common mistake is to forget to calculate the probability of Yanga and Barcelona winning and instead using the probability of Simba and Real Madrid to calculate the final probability.
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