Question

A coin is flipped and the spinner atthe right is spun. Find eachprobability.

Answer 1

We are given a coin and a spinner with four colors. We are asked the following:

`P(heads\text{ and yellow\rparen}`

To determine this probability we will use the following relationship:

`P(A\text{ and B\rparen= P\lparen A\rparen *P\lparen B\rparen}`

Applying the relationship we get:

`P(heads\text{ and yellow\rparen=}P(heads)*P(yellow)`

The probability is given by the following:

`P=\frac{#desired\text{ outcomes}}{#outcomes}`

Therefore, the probability is the quotient between the number of desired outcomes and the number of possible outcomes.

In the case of the coin, the desired outcome is "heads" since there is only 1 possible outcome that by tossing the coin we would get heads this means:

`#desired\text{ outcomes = 1}`

Since there are two possible outcomes (head, Tails) this means:

`#outcomes\text{ = 2}`

Substituting in the formula for the probability we get:

`P(heads)=(1)/(2)`

Now, the probability of the spinner. Since that is only one possible outcome where the spinner is yellow and there are 4 possible outcomes we have:

`P(yellow)=(1)/(4)`

Now, we substitute the values in the formula for both probabilities:

Solving the operations:

`P(heads\text{ and yellow\rparen=}(1)/(8)=0.125`

Now, we are asked to determine the probability of:

`P(tails\text{ and not red\rparen}`

Applying the same relationship we get:

`P(tail\text{ and not red\rparen=P\lparen tail\rparen *P\lparen not red\rparen}`

Now, for the probability of "not red" we use the following relationship:

`P(not\text{ A\rparen=1-P\lparen A\rparen}`

Applying the relationship we get:

`P(tail\text{ and not red\rparen=P\lparen tail\rparen *\lparen1-P\lparen red\rparen\rparen}`

The probability of getting tail is:

`P(tail)=(1)/(2)`

The probability of getting red is determined having into account that there are 2 possible outcomes for the spinner to be red:

`P(red)=(2)/(4)=(1)/(2)`

Substituting in the formula for both probabilities:

`P(tail\text{ and not red\rparen=}(1)/(2)*(1-(1)/(2))=(1)/(2)((1)/(2))=(1)/(4)=0.25`

Now, we are asked the following probability:

`P(tails\text{ and blue\rparen=P\lparen tails\rparen *P\lparen blue\rparen}`

The probability of getting tails was determined previously. The probability of getting blue is obtained having into account that there is 1 possible outcome for the spinner to be blue, therefore:

`P(blue)=(1)/(4)`

Substituting we get:

`P(tails\text{ and blue\rparen=}(1)/(2)*(1)/(4)=(1)/(8)=0.125`