Question

We perform the experiment "Toss two dice". What is the probability of the event "no 3 appears on either face"? We toss three coins. What is the probability of the event "3 Heads appear"?

Answer 1

Answer: 25/36, 1/8

Step-by-step explanation: For the first and second question: 25/36 because 5/6 represents the probability of not rolling a 3. Doing it twice in a row has us get (5/6)(5/6) = 25/36

2 sides per coin

3 coins

2^3 = 2*2*2 = 8 outcomes total when we flip three coins

The 8 outcomes are

HHH

HHT

HTH

HTT

THH

THT

TTH

TTT

We see that HHH, representing 3 heads in a row, only comes up 1 time out of 8 total

1/8 is the answer

Answer 2

A - the scenario when 3 appears at least once:

P(A) = 2/36 = 1/18

P(~A) = 1 - 1/18 = 17/18 - the probability 3 doesn't appear.

H - the scenario of 3 heads.

P(H) = P(One Heads)^3 = (1/2)^3 = 1/8