Smart people only...Help me with this question please...:(?

Question

Carol flips a coin and rolls a standard number cube 40 times each. How many times do you predict the outcome will be heads and a prime number?

Answer 1

Flipping a coin is a random event. There are essentially only two possible results or outcomes, heads and tails. Each is equally likely. If you flip a coin, there is as much chance, 50% that the outcome will be heads as it is that the outcome will be tails.

If a friend hands you a quarter and asks you to flip it, there is a 50% chance the outcome will be heads and a 50% chance the outcome will be tails. What if just before you were given the quarter your friend flipped the quarter ten times and the outcome was heads each time - would that change your likelihood of getting heads? No - nothing your friend did has any effect on the outcome when you flip the quarter. What if your friend flipped the quarter those ten times and got heads each time, and then decided to flip the quarter one more time. Is he or she more likely to get a tails on the eleventh try? No. Again, the previous outcomes have no effect on the next flip. Flipping a coin is a random event.

Rolling dice is also a random event. If we roll a single die there are six possible outcomes, one through six, all equally likely. Because rolling a die is a random event, it is possible to roll the die six different times and get the same number all six times. It is also possible to roll the die six different times and get each number once.

Each of the six numbers on a die is equally likely, but if we roll a die just six times we won't always get each number just once. If we roll the die sixty times we are going to come closer to getting each number with the same frequency. If we roll the die six hundred times we are going to come even closer to getting each number with the same frequency.

If one drew a graph of the frequency of each outcome of rolling a single die, the graph would tend to look like a horizontal line because each of the outcomes are equally likely.

But what if we are rolling a pair of dice and adding the two numbers to get a sum. Now the possible results are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. When the pair of dice is rolled, the first die can show any of six numbers, and for each of those results the second die can also show any of six numbers. Therefore there are a total of 36 possible pairs. We are interested in the sum of the two dice, and there are 11 possible sums. Are they all equally likely? Out of the 36 possible pairs of numbers, only one will produce a sum of 2 (1 and 1). Out of the 36 possible pairs of numbers, five different ones will produce a sum of 6 (1 and 5, 2 and 4, 3 and 3, 4 and 2, and 5 and 1). The outcomes and their expected frequencies are:
Sum. 2 3 4 5 6 7 8 9 10 11 12
Freq. 1 2 3 4 5 6 5 4 3 2 1
Again if we roll a pair of dice just 36 times it is unlikely we would get exactly the distribution expected. But if we roll a pair of dice 360 or 3600 times we would come much closer to the expected results.

Answer 2

well, she'll flip heads 50% of the time, so she's got a 1 in 2 chance of flipping heads. and a die has the numbers 1-6 on it. 1,2, and 5 are prime, so that would mean she has a 3 in 6, or 1in 2 chance of rolling a prime number. So, to find out the probability of flipping heads and rolling a prime number at the same time, you'd multiply the two probabilities together: 1/2 x 1/2=1/4. that means 1/4 of the time, she'll get heads and a prime number. since she did it 40 times, that means she'll get heads and a prime 10 times.

Answer 3

probability of getting head is 1/2
probability of geting a number that is prime is 3/6 or 1/2

1/2 * 1/2 = 1/4

you roll 40 times

40 * 1/4 = 10

Answer 4

I could predict any number I wanted, it need not be based on statistics.

I suppose there is some debate about whether or not I am smart.

My prediction? It will happen somewhere between 0 and 40 times.

(Note, I consider 1 to be a prime number so my prediction may be a little bit off if you don't consider 1 to be prime.)

Answer 5

20/26.4

A coin, only having two sides, has a 50% chance of landing on heads and a 50% chance of landing on tails.

A standard die has 6 sides; with 4 of those numbers being prime (not easily divisible by other numbers: 1, 2, 3, 5), so has a 66% chance of landing on a prime number. 66% of 40 is 26.4.

Answer 6

20 times heads and 27 times prime

Answer 7

coin expect 40 * 0.5 = 20
40 * (1/6 + 1/6 + 1/6) = 20
1/6 for 2, 3 and 5

Answer 8

you asked smart people to help you with this question... a little rude don't you think...

anyways, enjoy trying to find out the answer... i know it but i am not smart ;)