Can Someone Help Me with These Word Problems?

[Guest]

1) Three fair coins are tossed. Find the probability of getting the same thing on all three coins.

2) Find the probability of a royal flush (5 highest cards of a single suit) in poker with a 52-card deck. (hint: in poker aces are high or low and a bridge hand is made up of 13 cards.)

3) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years.

4) Is this mutually exclusive? Being a teenager and being a U.S. Senator

5) Is this mutually exclusive? Wearing a coat and wearing a sweater

 

[happy]

What have you done on these?

 

[pka]

What have YOU done on any of these?
Please reply with some effort.

 

[tkhunny]

1) Three fair coins are tossed. Find the probability of getting the same thing on all three coins.

Are the coins the same? If so, the probability of being the same is 100%. :lol:

 

[soroban]

Hello, Anonymous!

Okay, since you're a newcomer, I'll explain these . . .

1) Three fair coins are tossed.
Find the probability of getting the same thing on all three coins.

With three coins, there are eight outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.
In two of them (HHH, TTT), the three coins turn up the same.
\(\displaystyle \;\;\)Therefore, the probability is: \(\displaystyle \,\frac{2}{8}\,=\,\frac{1}{4}\)

2) Find the probability of a royal flush (5 highest cards of a single suit) in poker
with a 52-card deck. \(\displaystyle \;\)(Hint: in poker, aces are high or low.)

There are: \(\displaystyle \,\begin{pmatrix}52\\5\end{pmatrix}\,=\,\frac{52!}{5!\cdot47!} \,-\,2598,960\) possible poker hands.

There are exactly four Royal Flushes: 10 through Ace in each of four suits.

Therefore: \(\displaystyle \,P(\text{Royal Flush})\:=\:\frac{4}{2,598,960}\:=\:\frac{1}{649,740}\)

3) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years.

There are 31 possible birthdays in May.
Hence, there are: \(\displaystyle \.365\,-\,31\:=\:334\) possible birthdays which are not in May.

Therefore: \(\displaystyle \,P(\text{b'day not in May})\:=\:\frac{334}{365}\)

4) Is this mutually exclusive: \(\displaystyle \;\)being a teenager and being a U.S. Senator?

"Mutually exclusive" means they cannot happen at the same time.

There is a minimum age to serve in the U. S. Senate.
Hence, a teenager cannot be a Senator.

Therefore, they are mutually exclusive.

5) Is this mutually exclusive: wearing a coat and wearing a sweater?

No, you can wear a coat and a sweater at the same time.