Probability of coin tosses and rolling dice

Question

So I am struggling on how to calculate probability with coins and dice, so with these next examples if you could explain it, it would be very helpful to me! Any help is appreciated.

Q: Find the probability of getting 1 head and 4 tails on 5 coin tosses

Q: Find the probability of getting 4 heads when 4 coins are tossed

Q: Find the odds in favor of rolling two consecutive odd numbers when a pair of dice is rolled.

Answer 1

Question 1

When tossing a coin, the probability of getting a head is .50. The probability of getting a tail is .50.

When we are looking for the probability of getting 1 head on 5 coin tosses, we are looking for the probability of 5 occurrences:

Head (.50) and Not Head (.50) and Not Head (.50) and Not Head (.50) and Not Head (.50)

(These probabilities are multiplied)

So we have

(.50)¹ (.50)⁴

We also have to multiply the number of combinations of 1 head out of 5 coin tosses

₅C₁ = 5

So all together we have

5•(.50)¹ (.50)⁴ = .15625 There is a 15.625% chance of getting 1 head (and 4 tails) on 5 coin tosses.

Question 2

Getting 4 heads when 4 coins are flipped

We are looking for the probability of:

Head (.50) and Head (.50) and Head (.50) and Head (.50)

So we have

(.50)⁴

We also have to multiply the number of combinations of 4 heads out of 4 coin tosses

₄C₄ = 1

So all together we have

1•(.50)⁴ = .0625 There is a 6.25% chance of getting 4 heads out of 4 coin tosses

Question 3

The odds in favor of rolling two consecutive odd numbers when a pair of dice is rolled

The probability of rolling an odd number is 3/6 or .50

So we are looking for the following probability:

Odd (.50) and Odd (.50)

So we have:

(.50)•(.50) = .25 There is a 25% chance of rolling two consecutive odd numbers when a pair of dice is rolled.

Answer 2

1) THere are 32 possible outcomes upon flipping 5 coins; The HEAD can appear in one of five positions, so 5/32

2) (1/2)^4 = 1/16

3) the probability of two odds is 1/4 , so 1 to 5 in favor