Question

Fred flips a coin, spins the spinner, and rolls a standard number cube. Find the probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three.

Answer 1

1/18

Explanation:

Write the ratio of the number of ways the event can occur to the number of possible outcomes. Use the Fundamental Counting Principle to find the number of possible outcomes. There are 2 possible outcomes for the first part (heads, tails), there are 3 possible outcomes for the second part (green, blue, yellow), and 6 possible outcomes for the third part (1, 2, 3, 4, 5, 6). Multiply to find the total number of possible outcomes:

(2)(3)(6) = 36

There are 2 ways for the event to occur:

1) the coin shows tails, the spinner lands on yellow, and the cube shows 3

2) the coin shows tails, the spinner lands on green, and the cube shows 3

Thus, there are 2 ways for the event to occur and there are 36 possible outcomes.

P(tails, yellow, green, three) = 2/36 = 1/18

Answer 2

The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three is
`(4)/(3)`

Explanation:

Given : Fred flips a coin, spins the spinner, and rolls a standard number cube.

To find : The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three ?

Solution :

First we find probability one by one,

1) Flips a coin - Head, Tail

Total number of outcome = 2

Favorable outcome (getting a tail) = 1

Probability that the coin will show tails is
`P(T)=(1)/(2)`

2) Spins the spinner - yellow, green, blue

Total number of outcome = 3

Favorable outcome (land on yellow or green) = 2

Probability that the spinner will land on yellow or green
`P(S)=(2)/(3)`

3) Rolls a standard number cube - 1,2,3,4,5,6

Total number of outcome = 6

Favorable outcome (show a three) = 1

Probability that the cube will show a three
`P(C)=(1)/(6)`

The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three is

`P=P(T)+P(S)+P(C)`

`P=(1)/(2)+(2)/(3)+(1)/(6)`

`P=(3+4+1)/(6)`

`P=(8)/(6)`

`P=(4)/(3)`

Therefore, The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three is
`(4)/(3)`