Question

You toss 3 fair coins in the air at once.

a) List the sample space.
b) What is the probability of getting all 3 heads?
c) What is the probability of getting all 3 tails?
d) What is the probability of getting 1 head and 2 tails?
e) What is the probability of getting 1 tail and 2 heads?
f) What do the probabilities from parts b through e add up to?

Answer 1

The sample space for tossing 3 fair coins consists of 8 possible outcomes. The probability of any specific outcome, such as getting all heads or all tails, is 1/8, while the probabilities of getting mixed results are higher. The total of these probabilities adds up to 1, representing the certainty that one of the enumerated outcomes will occur.

Step-by-step explanation:

Sample Space and Probabilities for Tossing 3 Fair Coins

When you toss 3 fair coins, the sample space consists of the following 8 outcomes:

HHH

HHT

HTH

HTT

THH

THT

TTH

TTT

Probability of getting all 3 heads (HHH) is 1/8 or 12.5% (since there is only one such outcome in the sample space).

Probability of getting all 3 tails (TTT) is also 1/8 or 12.5% for the same reason.

Probability of getting 1 head and 2 tails (HTT, THT, TTH) is 3/8 or 37.5% because there are three such outcomes in the sample space.

Probability of getting 1 tail and 2 heads (THH, HTH, HHT) is again 3/8 or 37.5% due to there being three possibilities for this outcome.

The probabilities from parts b through e add up to 1/8 + 1/8 + 3/8 + 3/8 which equals 8/8, or 1, signifying all the possible outcomes have been accounted for.

Answer 2

B, 51% (Everyone thinks it;s 50/50 but it's actually 51%.
C,49%
D,39%
E,40%
F,I'm confused now....LOL

But I did not pick random numbers I did it with a tool I programmed myself. But it's still buggy so these chances might not even be correct. But when it's done I will send it to you if you want.