Question

You have a bucket with 500 coins. 499 of them are normal coins, but one of them is double headed. You pick a coin randomly from this bucker and flip it 5 times. If you picked a normal coin, what would be the probability of flipping 5 heads?

Answer 1

Answer:

If a normal coin is picked then probability of flipping 5 heads = 0.031

Step-by-step explanation:

Given:

Number of coins = 500

Number of normal coins =499

Number of double headed coin = 1

Event A:

Pick a normal coin

Probability of event A to occur $P(A)=\frac{Number\ of\ normal\ coins}{Total\ number\ of\ coins} =\frac{499}{500}$

Event B:

Normal coin is flipped 5 times to get head.

Probability of flipping one head at a time = $\frac{1}{2}$

Probability of event B to occur (flipping 5 heads)

P(B) =$\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{32}$  

Probability of event A and B to occur together $=P(A)\times P(B)=\frac{499}{500}\times \frac{1}{32}=0.031$

If a normal coin is picked then probability of flipping 5 heads = 0.031