Blakemiller2020
30.11.2019 •
Mathematics
Problem 17.4. to determine which of two people gets a prize, a coin is flipped twice. if the flips are a head and then a tail, the first player wins. if the flips are a tail and then a head, the second player wins. however, if both coins land the same way, the flips don’t count and the whole process starts over. assume that on each flip, a head comes up with probability p, regardless of what happened on other flips. use the four step method to find a simple formula for the probability that the first player wins. what is the probability that neither player wins?
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Ответ:
-First player wins:
-Neither player wins:
Step-by-step explanation:
Applying the 4 step method:
Step 1: Identify events for which probability is to be determined:
- First player wins: First coin is heads, second coin is tails (HT)
- Neither player wins: Both coins are heads or both coins are tails (HH or TT)
Step 2: Calculate total number of possible outcomes:
Four possible outcomes: HH, HT, TT, TH
Step 3: Calculate probability of each event
Since the probability of a coin coming up heads is 'p':
Step 4: Add probability of each event
-First player wins:
-Neither player wins:
Ответ: