Question

In a certain experiment, a coin is tossed and this spinner is spun. Computer the probability of the event. P(heads and blue)

Answer 1

The probability of the event P(heads and blue) can be found by multiplying the probability of getting heads on the coin toss by the probability of landing on blue on the spinner.

Step-by-step explanation:

The probability of the event P(heads and blue) can be found by multiplying the probability of getting heads on the coin toss by the probability of landing on blue on the spinner. Let's assume that the probability of getting heads on the coin toss is 0.5 and the probability of landing on blue on the spinner is 0.25.

P(heads and blue) = P(heads) * P(blue) = 0.5 * 0.25 = 0.125

Therefore, the probability of the event P(heads and blue) is 0.125 or 12.5%.

Answer 2

We are asked to determine the possibility of getting heads and getting blue from the spinner. This is represented as:

`P\mleft(\text{heads and blue}\mright)​`

Since we have the probability of two independent events happening at the same time the probability is the product of the probability of both each event, like this:

`P(\text{heads and blue})​=P(\text{head)xP(blue)}`

Now, we will determine each of the probabilities. We begin with the probability of getting head. The probability is the quotient between the desired events, in this case, 1 (heads), and the number of possible events, in this case, 2 (heads, tails). Therefore, the probability is:

`P(\text{head)}=(1)/(2)`

Now, we determine the probability of getting blue. The number of desired events is 1 (blue) and the number of possible events is 3 (blue, white, gray), therefore, the probability is:

`P(\text{blue)}=(1)/(3)`

Now, we substitute in the formula for the combined probabilities:

`P(\text{heads and blue})​=((1)/(2))*((1)/(3))=(1)/(6)`

Therefore, the probability of getting heads and blue is 1/6.