For each game, there are only two possible outcomes. Either you win at least $1, or you do not. Games are independent. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Probability of winning at least $1 on a single game:

The die has 6 sides.

If it lands on 4, 5 or 6(either of the three sides), you win at least $1. So

$p = \frac{1}{2} = 0.5$

You are going to play the game twice.

This means that $n = 2$

The probability that you win at least $1 both times is

This is P(X = 2).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{2,2}.(0.5)^{2}.(0.5)^{2} = 0.25$

The probability that you win at least $1 both times is 0.25 = 25%.

4 0

3 years ago

Point A is plotted at (-5, 3)

Diano4ka-milaya [45]

Answer:

quadrant 1

Step-by-step explanation:

quadrant 1 is (-,+)

5 0

3 years ago

At noon, the minute and the hour hands of a clock overlap. In how long will they again overlap?

kati45 [8]

Answer:

Okay. At noon, the hour and minute hand overlap. First, let’s calculate the speed of the hands.

The minute hand rotates once around the clock every hour. It goes 360 degrees in 60 minutes, so it rotates 360/60 or 6 degrees per minute. The hour hand goes once around the clock every 12 hours. Because there are 60 minutes in an hour, it goes 360 degrees 12*60 or 720 minutes. This means it travels at a speed of 360/720 or 0.5 degrees per minute.

Once the clock starts, the minute hand goes ahead and rotates ahead of the hour hand. At 1:00, the minute hand is at 12, and the hour hand is ahead at 1. This is where we will start our calculations.

Now, we have a variable, m, which is the minutes that have passed since the clock started. So, our minute hand speed is 6m, and our hour hand speed is 0.5m. However, because the hour hand is at one, it is at 30 degrees. (360/12 * 1.) This means our equation is 6m = 0.5m+30.

Now, we calculate.

6m = 0.5m+30

5.5m = 30

m = 30/5.5

m = 5.45

So at 5.45 minutes, the minute hand is at the hour hand. However, because one hour has passed since we started, we have to add on one hour.

So, our final total is 1 hour 5 minutes and 27 seconds.

Step-by-step explanation:

4 0

3 years ago

James earns 20 allowance every month and 30 for each a on his report card

Svetach [21]

Answer:

Part A - the independant variable is the monthly allowance, and the dependent amount is the one that he has to get As for in order to receive it.

Part B - y = 30x + 20

Step-by-step explanation:

7 0

3 years ago