Question

Probability Questions

You go into an icecream store and decide tou want 3 scoops of ice cream, there are 21 different flavors to choose from, how many combinations of three flavors are possible?

If you toss 10 coins how many different combinations could possibly give you 6 heads?

In the toss of 6 coins, what is the probability of obtaining exactly 2 heads?

In the toss of 5 dice, what is the probability of obtaining exactly 5 ones?

In the toss of 5 dice, what is the probability of obtaining 2 or fewer ones?

Answer 1

1.)

There are 3 possible cases:-

Case 1

All 3 scoops are of same flavour = Number of flavours available = 21 ways

Case 2

All 3 scoops are different =

= (21*20*19) /6

= 7*10*19

= 1330 ways

Case 3

2 scoops of same flavour and 1 scoop of different flavour

There will be 21 ways to select the flavour that has 2 sccops and 20 (21-1) ways to select the different flavour as we cannot choose what we have choosen for 2 scoops.

So,

Number of ways of choosing 2 scoops of same flavour and 1 scoop of different flavour = 21* 20 = 210 ways

Since, these are all possibilities. So, total combinations = 21 + 1330 + 210 = 1561 ways

Binomial formula for getting r success in n turns

= *(Probability of getting success) ^r * (Probability of getting failure) ^{n - r}

2.)

6 heads in 10 toss =

3.)

2 heads in 6 toss =

4.)

5 ones in 5 dice throw =