Question

1. Flip a fair coin ten times. Find the probability of at least seven heads.

2. Draw five cards at once from a deck. Find the probability of getting two pairs.

3. Roll a die infinitely times. Find the probability that you see an even number before you see an one.

4. You and your friend take turns to draw from an urn containing one green marble and one hundred blue marbles, one at a time and you keep the marble. Whoever draw the green marble wins. Suppose you draw first. What is the probability that you win?

Answer 1

1

When a fair coin is tossed probability of getting a head is p = 0.50.

Let X is a random variable shows the number of heads in 10 tosses. Here X has binomial distribution with parameters as follows:

n =10 and p=0.5

The probability of at least seven heads is

2:

There are total 13 denominations and each denomination has 4 cards. So number of ways of selecting 2 denominations and then 2 cards out of 4 is

And since we need exactly 2 pairs so remaining 1 card must come from different denomination so number of ways of selecting 1 denominations out of remaining 11 denominations and then 1 card from selected denomination is

So number of ways of selecting 2 pairs is :

So required probability is