Chapter 7, Problem 2PT2

To determine

The correct answer from the options that the probability of getting at least one tail in four tosses of a coin is (a) 0.2500, (b) 0.3125, (c) 0.6875, (d) 0.9375, (e) none of these.

Answer to Problem 2PT2

The correct answer is (a).

Explanation of Solution

Given information:

The probability distribution:

  

The above distribution gives the probabilities for 4 number of heads.

These probabilities have at least one occurrence of tails over the 4 coin tosses.

Write the probabilities as:

  $P\left(0\right)=0.0625$

  $P\left(1\right)=0.2500$

  $P\left(2\right)=0.3750$

  $P\left(3\right)=0.2500$

To find the probability of getting at least one tail in four tosses, add $P\left(0\right)$ , $P\left(1\right)$ , $P\left(2\right)$ and $P\left(3\right)$ .

  $\begin{array}{c}P\left(0\right)+P\left(1\right)+P\left(2\right)+P\left(3\right)=0.0625+0.2500+0.3750+0.2500\\ =0.9375\end{array}$

Hence, the correct answer is (d).