A bag of poker chips contains 4 purple, 6 red, 3 pink, and 2 black chips. What is the probability of pulling from the bag:
The correct answer and explanation is:
To determine the probability of pulling a specific chip from the bag, we first need to know the total number of chips in the bag.
The total number of chips is:
- 4 purple chips
- 6 red chips
- 3 pink chips
- 2 black chips
Adding these up:
4 + 6 + 3 + 2 = 15 total chips.
The probability of an event is calculated using the formula: P(Event)=Number of favorable outcomesTotal number of possible outcomesP(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
Example 1: Probability of pulling a purple chip
The number of purple chips is 4. So, the probability of drawing a purple chip is: P(Purple)=415P(\text{Purple}) = \frac{4}{15}
This means that the probability of pulling a purple chip is 415\frac{4}{15}.
Example 2: Probability of pulling a red chip
The number of red chips is 6. Therefore, the probability of drawing a red chip is: P(Red)=615=25P(\text{Red}) = \frac{6}{15} = \frac{2}{5}
This shows that the probability of drawing a red chip is 25\frac{2}{5}.
Example 3: Probability of pulling a pink chip
The number of pink chips is 3. Hence, the probability of drawing a pink chip is: P(Pink)=315=15P(\text{Pink}) = \frac{3}{15} = \frac{1}{5}
So, the probability of pulling a pink chip is 15\frac{1}{5}.
Example 4: Probability of pulling a black chip
The number of black chips is 2. Therefore, the probability of drawing a black chip is: P(Black)=215P(\text{Black}) = \frac{2}{15}
So, the probability of pulling a black chip is 215\frac{2}{15}.
In summary, the total number of chips is 15, and the probabilities of pulling a purple, red, pink, or black chip are as calculated above. The total probability for all possible events should sum to 1, as the sum of all possible outcomes must equal certainty.