There are four boxes .Each box contains two balls .One red and one blue .You draw one ball from each of the four boxes.
What is the probability of drawing at least one red ball ?

Options

A. A)`13//16`
B. B)`15//16`
C. C)`9//16`
D. D)`11//16`

Answer

To solve the problem of finding the probability of drawing at least one red ball from four boxes, each containing one red and one blue ball, we can follow these steps:

### Step 1: Understand the setup
Each of the four boxes contains:
- 1 Red Ball
- 1 Blue Ball

When we draw one ball from each box, we have a total of four draws.

### Step 2: Calculate the probability of drawing a blue ball from each box
The probability of drawing a blue ball from one box is:
\[ P(\text{Blue from one box}) = \frac{1}{2} \]

Since the draws are independent, the probability of drawing a blue ball from all four boxes is:
\[ P(\text{All Blue}) = P(\text{Blue from Box 1}) \times P(\text{Blue from Box 2}) \times P(\text{Blue from Box 3}) \times P(\text{Blue from Box 4}) \]
\[ P(\text{All Blue}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \left(\frac{1}{2}\right)^4 = \frac{1}{16} \]

### Step 3: Calculate the probability of drawing at least one red ball
To find the probability of drawing at least one red ball, we can use the complement rule:
\[ P(\text{At least one Red}) = 1 - P(\text{All Blue}) \]
\[ P(\text{At least one Red}) = 1 - \frac{1}{16} = \frac{15}{16} \]

### Final Answer
Thus, the probability of drawing at least one red ball when one ball is drawn from each of the four boxes is:
\[ \frac{15}{16} \]