Sure, let's go through this step-by-step.
### Step 1: Understand the given information
- Total number of games played: 30
- Number of games A won: 20
- Number of drawn games: 2
We need to find:
- (a) The probability that A wins.
- (b) The probability that B does not lost (which means either B wins or the game is drawn).
### Step 2: Calculate the number of games B won
First, since the number of games A won and the number of drawn games are given, we can find the number of games B won by subtracting these from the total number of games:
[tex]\[ B \text{ wins} = \text{Total games} - \text{A wins} - \text{Draws} \][/tex]
Substituting the values we have:
[tex]\[ B \text{ wins} = 30 - 20 - 2 = 8 \][/tex]
So, B won 8 games.
### Step 3: Calculate the probabilities
#### (a) Probability that A wins
The probability of A winning is given by the ratio of the number of games A won to the total number of games played:
[tex]\[ \text{Probability of A winning} = \frac{\text{Number of games A won}}{\text{Total number of games}} \][/tex]
[tex]\[ \text{Probability of A winning} = \frac{20}{30} = \frac{2}{3} \approx 0.6667 \][/tex]
#### (b) Probability that B does not lose
B does not lose if either B wins or the game is drawn. We need to find the total number of games either won by B or drawn and divide it by the total number of games played.
[tex]\[ \text{B wins or Draws} = B \text{ wins} + \text{Draws} \][/tex]
[tex]\[ \text{B wins or Draws} = 8 + 2 = 10 \][/tex]
So, the probability that B does not lose is:
[tex]\[ \text{Probability of B not losing} = \frac{\text{Number of games B won or drawn}}{\text{Total number of games}} \][/tex]
[tex]\[ \text{Probability of B not losing} = \frac{10}{30} = \frac{1}{3} \approx 0.3333 \][/tex]
### Final Answer:
(a) The probability that A wins is approximately 0.6667 (or 66.67%).
(b) The probability that B does not lose is approximately 0.3333 (or 33.33%).
