Question

Use the "at least once" rule to find the probabilities of the following event.Getting at least one head when tossing four fair coinsQuestion content area bottomPart 1The probability isenter your response here.(Type an integer or a simplified fraction.)

Answer 1

The Probability of getting at least one head when tossing four fair coins is 15/16

Step-by-step explanation:

A coin as a head and a tail

Probability of getting a head = 1/2

Probability of getting a tail = 1 - 1/2 = 1/2

We need to find the probability of getting at least 1 head when tossing 4 coins.

To do this, we will apply the "at least once" rule

At least once rule states that:

`\begin{gathered} Pr(at\text{ least 1head\rparen= 1 - \lparen Pr\lparen no head\rparen\rparen}^n \\ where\text{ n = number of times the fair coin was tossed} \end{gathered}`
`\begin{gathered} Pr(no\text{ head\rparen = Pr\lparen tail\rparen = 1/2} \\ n\text{ = 4} \\ \\ Pr(at\text{ least 1 head\rparen = 1-\lparen}(1)/(2))^4 \\ Pr(at\text{ least 1 head\rparen= 1- }(1)/(2^4)\text{ = 1-}(1)/(16) \\ Pr(at\text{ least 1 head\rparen = }(16-1)/(16) \\ \\ Pr(at\text{ least 1 head\rparen =}(15)/(16) \end{gathered}`