Question

Three different coins are tossed. What is P(tail, head or tail, head, or tail)

Answer 1

Answers:

Probability of landing all three coins on head:
`(1)/(8)`

Probability of landing all three coins on tail:
`(1)/(8)`

Probability of landing two coins on head and one on tail:
`(3)/(8)`

Probability of landing two coins on tails and one on head:
`(3)/(8)`

Step-by-step explanation (Read Carefully):

-How to calculate this is that there are three possible outcomes when tossing the three coins. So, if you group all the possible outcomes of heads and tails when tossing the three coins in one event, you’ll get eight events. Let’s take a look at it:

-A way to organize this is to have:

H = heads

T = tails

-Total of eight events, where each event is the probability of the three coins being tossed (possible events with equal probability, and order matters):

HHH

HHT

HTH

HTT

THH

THT

TTH

TTT

Now, let’s apply some questions:

⇒ Probability of landing all three coins on heads:
`(1)/(8)`

Step-by-step explanation: Look at the events above. How many times (out of the eight events) that all three coins land on heads? Well, you can see that there is only one possible event that has HHH. So, the probability of landing all three coins on heads (out of the eight events) is
`(1)/(8)`.

⇒ Probability of landing all three coins on tails:
`(1)/(8)`

Step-by-step explanation: Look at the events above. How many times (out of the eight events) that all three coins land on tails? Well, you can see that there is only one possible event that has TTT. So, the probability of landing all three coins on tails (out of the eight events) is
`(1)/(8)`.

⇒ Probability of landing two coins on heads and one on tails:
`(3)/(8)`

Step-by-step explanation: Look at the events above. How many times (out of the eight events) where two coins land on heads and one on tails? Well, you can see that there are three possible events that include HHT, HTH, THH. So, the probability of landing two coins on heads and one on tails (out of the eight events) is
`(3)/(8)`.

⇒ Probability of landing two coins on tails and one on heads:
`(3)/(8)`

Step-by-step explanation: Look at the events above. How many times (out of the eight events) where two coins land on tails the one on heads? Well, you can see that there are three possible events that include HTT, THT, TTH. So, the probability of landing two coins on tails and one on heads (out of the eight events) is
`(3)/(8)`.

I hope you understand and that this helps with your question! :)