Roger Federer and Raphael Nadal are playing the final of Wimbledon's tennis tournament.
If Federer wins the first set then he has 8 chances in 10 to win the match.
If Nadal wins the first set then he has one chance in 2 to win the match.
Nadal has only 3 chances in 10 to win the first set, what is the probability that he wins the match ? |

In the same way, the event 'Nadal wins the first set then wins the match' is the event . Its probability is equal to .

Finally, the probability Nadal wins the match is equal to the sum of the two probabilities we have just calculated, it is the

Raphael Nadal has a little less than 3 chances in 10 to win the match.

2. You pick up consequently 5 balls and put them back in the box after you pick up each of them. What is the probability that you draw 5 red balls? The answer is

Probabilities are multiplying.

3. You pick up consequently 3 balls without putting them again in the box. What is the probability that you get 2 green ones and a red one? You must examine all cases which lead to the result and add their probabilities. You can pick up VVR, VRV ou RVV hence the probability is :

4. How many different ways are there to draw simultaneously 3 balls in the box (for example draw the balls 123, 125, 345, but not 132 because it was counted already)?

The answer is number . It's the number of subsets of 3 elements contained in a set of 5 elements. You calculate it with the formula :

Number n! reads 'factorial n'.

There are 10 different ways.

5. You draw 3 balls simultaneously. What is the probability that you draw 2 green ones and one red (event E)? The number of favorable cases is equal to the number of possibilities to draw 2 green ones among 3 green ones multiplied by the number of possibilities to draw one red ball among the 2 red ones. The total number of cases is 10 (question 4). The detailed calculation is as follows :