Suyash needs his calculator for his mathematics lesson . It is either in his pocket , bag or locker . The probability it is in his pocket is 0.20 , the probability it is in his bag is 0.58 . What is the probability that it is in his locker ?

Answer

To find the probability that Suyash's calculator is in his locker, we can follow these steps:

### Step 1: Understand the total probability
The total probability of all possible outcomes must equal 1. In this case, the outcomes are:
- The calculator is in his pocket
- The calculator is in his bag
- The calculator is in his locker

### Step 2: Write down the given probabilities
We know:
- Probability that the calculator is in his pocket (P(Pocket)) = 0.20
- Probability that the calculator is in his bag (P(Bag)) = 0.58

### Step 3: Set up the equation for total probability
Let P(Locker) be the probability that the calculator is in his locker. According to the total probability rule:
\[ P(Pocket) + P(Bag) + P(Locker) = 1 \]

Substituting the known values into the equation:
\[ 0.20 + 0.58 + P(Locker) = 1 \]

### Step 4: Simplify the equation
Combine the probabilities of the pocket and bag:
\[ 0.20 + 0.58 = 0.78 \]
So, the equation becomes:
\[ 0.78 + P(Locker) = 1 \]

### Step 5: Solve for P(Locker)
To find the probability that the calculator is in the locker, we rearrange the equation:
\[ P(Locker) = 1 - 0.78 \]
\[ P(Locker) = 0.22 \]

### Conclusion
The probability that Suyash's calculator is in his locker is **0.22**.

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